Edit Profile (opens in new tab) Birkar, Caucher Co-Author Distance Author ID: birkar.caucher Published as: Birkar, Caucher; Birkar, C. Further Spellings: Bîrkar, Koçer; Derakhshani, Fereydoun Homepage: https://www.dpmms.cam.ac.uk/~cb496/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Awards: Fields Medal (2018) Documents Indexed: 52 Publications since 2003, including 19 Additional arXiv Preprints 2 Contributions as Editor · 1 Further Contribution Biographic References: 6 Publications Co-Authors: 34 Co-Authors with 21 Joint Publications 719 Co-Co-Authors all top 5 Co-Authors 33 single-authored 4 Chen, Yifei 3 Cheltsov, Ivan Anatol’evich 2 Bogomolov, Fedor Alekseivich 2 Hacon, Christopher Derek 2 Hu, Zhengyu 1 Alexeev, Valery A. 1 Cascini, Paolo 1 Chen, Jungkai Alfred 1 Di Cerbo, Gabriele 1 Gorchinskiĭ, Sergeĭ Olegovich 1 Ishii, Shihoko 1 Katzarkov, Ludmil 1 Liu, Jihao 1 Loginov, Konstantin Konstantinovich 1 McKernan, James 1 Nikulin, Vyacheslav Valentinovich 1 Oguiso, Keiji 1 Orlov, Dmitri O. 1 Parshin, Alekseĭ Nikolaevich 1 Parshin, Yu. G. 1 Paun, Mihai 1 Prokhorov, A. N. 1 Prokhorov, Yuriĭ Gennad’evich 1 Qu, Santai 1 Reid, Miles 1 Shokurov, Vyacheslav Vladimirovich 1 Shramov, Konstantin Aleksandrovich 1 Svaldi, Roberto 1 Takayama, Shigeharu 1 Tikhomirov, Alexander Sergeevich 1 Waldron, Joe 1 Zarkhin, Yuriĭ Gennad’evich 1 Zhang, De-Qi 1 Zhang, Lei all top 5 Serials 4 Journal für die Reine und Angewandte Mathematik 3 Compositio Mathematica 3 Publications Mathématiques 3 Mathematische Annalen 2 Advances in Mathematics 2 Nagoya Mathematical Journal 2 Sbornik: Mathematics 2 Annals of Mathematics. Second Series 2 ICCM Notices 1 Russian Mathematical Surveys 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Duke Mathematical Journal 1 Gazette des Mathématiciens 1 Journal of the Mathematical Society of Japan 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Journal of the American Mathematical Society 1 Journal of Algebraic Geometry 1 Advanced Studies in Pure Mathematics 1 Algebra & Number Theory 1 EMS Surveys in Mathematical Sciences Fields 35 Algebraic geometry (14-XX) 5 History and biography (01-XX) 3 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 30 Publications have been cited 1,062 times in 657 Documents Cited by ▼ Year ▼ Existence of minimal models for varieties of log general type. Zbl 1210.14019 Birkar, Caucher; Cascini, Paolo; Hacon, Christopher D.; McKernan, James 521 2010 Anti-pluricanonical systems on Fano varieties. Zbl 1470.14078 Birkar, Caucher 66 2019 Singularities of linear systems and boundedness of Fano varieties. Zbl 1469.14085 Birkar, Caucher 61 2021 Existence of log canonical flips and a special LMMP. Zbl 1256.14012 Birkar, Caucher 52 2012 Existence of flips and minimal models for 3-folds in char \(p\). Zbl 1346.14040 Birkar, Caucher 45 2016 Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Zbl 1348.14038 Birkar, Caucher; Zhang, De-Qi 41 2016 Singularities on the base of a Fano type fibration. Zbl 1348.14037 Birkar, Caucher 40 2016 Existence of Mori fibre spaces for 3-folds in char \(p\). Zbl 1373.14019 Birkar, Caucher; Waldron, Joe 34 2017 On existence of log minimal models. II. Zbl 1226.14021 Birkar, Caucher 23 2011 Ascending chain condition for log canonical thresholds and termination of log flips. Zbl 1109.14018 Birkar, Caucher 23 2007 On existence of log minimal models. Zbl 1197.14011 Birkar, Caucher 20 2010 The Iitaka conjecture \(C _{n, m}\) in dimension six. Zbl 1186.14015 Birkar, Caucher 17 2009 On existence of log minimal models and weak Zariski decompositions. Zbl 1255.14016 Birkar, Caucher 16 2012 The augmented base locus of real divisors over arbitrary fields. Zbl 1388.14054 Birkar, Caucher 16 2017 Varieties fibred over abelian varieties with fibres of log general type. Zbl 1308.14014 Birkar, Caucher; Chen, Jungkai Alfred 13 2015 Polarized pairs, log minimal models, and Zariski decompositions. Zbl 1314.14028 Birkar, Caucher; Hu, Zhengyu 11 2014 Generalised pairs in birational geometry. Zbl 1471.14035 Birkar, Caucher 11 2021 Log canonical pairs with good augmented base loci. Zbl 1314.14027 Birkar, Caucher; Hu, Zhengyu 8 2014 Log minimal models according to Shokurov. Zbl 1194.14021 Birkar, Caucher 7 2009 Iitaka \(C_{n,m}\) conjecture for 3-folds over finite fields. Zbl 1423.14219 Birkar, Caucher; Chen, Yifei; Zhang, Lei 7 2018 Mld’s vs thresholds and flips. Zbl 1194.14020 Birkar, C.; Shokurov, V. V. 6 2010 Log canonical algebras and modules. Zbl 1291.14030 Birkar, Caucher 6 2013 Images of manifolds with semi-ample anti-canonical divisor. Zbl 1343.14012 Birkar, Caucher; Chen, Yifei 5 2016 On termination of log flips in dimension four. Zbl 1184.14026 Birkar, Caucher 3 2010 Geometry of polarised varieties. Zbl 07692198 Birkar, Caucher 3 2023 Minimal models, flips and finite generation: a tribute to V.V. Shokurov and Y.-T. Siu. Zbl 1219.14021 Birkar, C.; Păun, M. 2 2011 Birational geometry of algebraic varieties. Zbl 1441.14053 Birkar, Caucher 2 2018 Singularities on toric fibrations. Zbl 1473.14004 Birkar, Caucher; Chen, Yifei 2 2021 Bounding non-rationality of divisors on 3-fold Fano fibrations. Zbl 1485.14028 Birkar, Caucher; Loginov, Konstantin 1 2021 Interview with Caucher Birkar. (\(\dots\) avec Caucher Birkar.) Zbl 1409.01054 Octavia, G. 1 2019 Geometry of polarised varieties. Zbl 07692198 Birkar, Caucher 3 2023 Singularities of linear systems and boundedness of Fano varieties. Zbl 1469.14085 Birkar, Caucher 61 2021 Generalised pairs in birational geometry. Zbl 1471.14035 Birkar, Caucher 11 2021 Singularities on toric fibrations. Zbl 1473.14004 Birkar, Caucher; Chen, Yifei 2 2021 Bounding non-rationality of divisors on 3-fold Fano fibrations. Zbl 1485.14028 Birkar, Caucher; Loginov, Konstantin 1 2021 Anti-pluricanonical systems on Fano varieties. Zbl 1470.14078 Birkar, Caucher 66 2019 Interview with Caucher Birkar. (\(\dots\) avec Caucher Birkar.) Zbl 1409.01054 Octavia, G. 1 2019 Iitaka \(C_{n,m}\) conjecture for 3-folds over finite fields. Zbl 1423.14219 Birkar, Caucher; Chen, Yifei; Zhang, Lei 7 2018 Birational geometry of algebraic varieties. Zbl 1441.14053 Birkar, Caucher 2 2018 Existence of Mori fibre spaces for 3-folds in char \(p\). Zbl 1373.14019 Birkar, Caucher; Waldron, Joe 34 2017 The augmented base locus of real divisors over arbitrary fields. Zbl 1388.14054 Birkar, Caucher 16 2017 Existence of flips and minimal models for 3-folds in char \(p\). Zbl 1346.14040 Birkar, Caucher 45 2016 Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Zbl 1348.14038 Birkar, Caucher; Zhang, De-Qi 41 2016 Singularities on the base of a Fano type fibration. Zbl 1348.14037 Birkar, Caucher 40 2016 Images of manifolds with semi-ample anti-canonical divisor. Zbl 1343.14012 Birkar, Caucher; Chen, Yifei 5 2016 Varieties fibred over abelian varieties with fibres of log general type. Zbl 1308.14014 Birkar, Caucher; Chen, Jungkai Alfred 13 2015 Polarized pairs, log minimal models, and Zariski decompositions. Zbl 1314.14028 Birkar, Caucher; Hu, Zhengyu 11 2014 Log canonical pairs with good augmented base loci. Zbl 1314.14027 Birkar, Caucher; Hu, Zhengyu 8 2014 Log canonical algebras and modules. Zbl 1291.14030 Birkar, Caucher 6 2013 Existence of log canonical flips and a special LMMP. Zbl 1256.14012 Birkar, Caucher 52 2012 On existence of log minimal models and weak Zariski decompositions. Zbl 1255.14016 Birkar, Caucher 16 2012 On existence of log minimal models. II. Zbl 1226.14021 Birkar, Caucher 23 2011 Minimal models, flips and finite generation: a tribute to V.V. Shokurov and Y.-T. Siu. Zbl 1219.14021 Birkar, C.; Păun, M. 2 2011 Existence of minimal models for varieties of log general type. Zbl 1210.14019 Birkar, Caucher; Cascini, Paolo; Hacon, Christopher D.; McKernan, James 521 2010 On existence of log minimal models. Zbl 1197.14011 Birkar, Caucher 20 2010 Mld’s vs thresholds and flips. Zbl 1194.14020 Birkar, C.; Shokurov, V. V. 6 2010 On termination of log flips in dimension four. Zbl 1184.14026 Birkar, Caucher 3 2010 The Iitaka conjecture \(C _{n, m}\) in dimension six. Zbl 1186.14015 Birkar, Caucher 17 2009 Log minimal models according to Shokurov. Zbl 1194.14021 Birkar, Caucher 7 2009 Ascending chain condition for log canonical thresholds and termination of log flips. Zbl 1109.14018 Birkar, Caucher 23 2007 all cited Publications top 5 cited Publications all top 5 Cited by 486 Authors 29 Xu, Chenyang 23 Birkar, Caucher 21 Fujino, Osamu 19 Zhang, De-Qi 16 Hacon, Christopher Derek 14 Cascini, Paolo 13 Han, Jingjun 13 Lazić, Vladimir 12 Gongyo, Yoshinori 11 Kollár, János 10 Hashizume, Kenta 10 Peternell, Thomas Martin 9 Fujita, Kento 9 Guedj, Vincent 9 Moraga Saez, Joaquín Leonardo 9 Paun, Mihai 9 Zeriahi, Ahmed 8 Casagrande, Cinzia 8 Guenancia, Henri 8 Liu, Jihao 8 Liu, Yuchen 8 Meng, Sheng 8 Prokhorov, Yuriĭ Gennad’evich 8 Witaszek, Jakub 8 Zhang, Lei 8 Zhuang, Ziquan 7 Andreatta, Marco 7 Bernasconi, Fabio 7 Blum, Harold 7 Jiang, Chen 7 Lehmann, Brian 7 Li, Chi 7 McKernan, James 7 Patakfalvi, Zsolt 7 Schwede, Karl E. 7 Tanaka, Hiromu 6 Boucksom, Sébastien 6 Campana, Frédéric 6 Chen, Guodu 6 Choi, Sung Rak 6 Codogni, Giulio 6 Druel, Stéphane 6 Filipazzi, Stefano 6 Höring, Andreas 6 Kebekus, Stefan 6 Kovács, Sándor J. 6 Svaldi, Roberto 5 Araujo, Carolina 5 Cheltsov, Ivan Anatol’evich 5 Di Cerbo, Gabriele 5 Eyssidieux, Philippe 5 Li, Zhan 5 Liu, Jie 5 Massarenti, Alex 5 Takagi, Shunsuke 5 Tanimoto, Sho 5 Totaro, Burt 5 Waldron, Joe 5 Zhou, Chuyu 4 Brown, Morgan V. 4 Cacciola, Salvatore 4 Chen, Jungkai Alfred 4 Chen, Meng 4 Chen, Yifei 4 Coskun, Izzet 4 de Fernex, Tommaso 4 Debarre, Olivier 4 Dubouloz, Adrien 4 Fontanari, Claudio 4 Greb, Daniel 4 Hassett, Brendan 4 Laface, Antonio 4 Liu, Haidong 4 Loginov, Konstantin Konstantinovich 4 Luo, Yujie 4 Mustaţă, Mircea 4 Nakamura, Yusuke 4 Namikawa, Yoshinori 4 Odaka, Yuji 4 Park, Jinhyung 4 Prendergast-Smith, Artie 4 Stigant, Liam 4 Taji, Behrouz 4 Tsakanikas, Nikolaos 4 Tschinkel, Yuri 4 Tucker, Kevin 4 Wang, Xiaowei 4 Xie, Lingyao 4 Yoshikawa, Shou 3 Alexeev, Valery A. 3 Braun, Lukas 3 Cao, Junyan 3 Catanese, Fabrizio M. E. 3 Dervan, Ruadhaí 3 Ein, Lawrence Man Hon 3 Fanelli, Andrea 3 Floris, Enrica 3 Galindo Pastor, Carlos 3 Graf, Patrick 3 Hausen, Jürgen ...and 386 more Authors all top 5 Cited in 120 Serials 39 Advances in Mathematics 36 Mathematische Annalen 33 Mathematische Zeitschrift 26 Compositio Mathematica 21 Annales de l’Institut Fourier 21 Duke Mathematical Journal 20 Transactions of the American Mathematical Society 19 Inventiones Mathematicae 16 Journal für die Reine und Angewandte Mathematik 16 Journal of Algebraic Geometry 15 Annals of Mathematics. Second Series 14 International Journal of Mathematics 14 European Journal of Mathematics 13 Nagoya Mathematical Journal 12 Manuscripta Mathematica 11 Journal of Algebra 11 Algebra & Number Theory 10 Selecta Mathematica. New Series 10 Forum of Mathematics, Sigma 9 Geometriae Dedicata 9 Journal of Pure and Applied Algebra 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 9 Journal of the European Mathematical Society (JEMS) 8 Mathematical Proceedings of the Cambridge Philosophical Society 8 Journal of the American Mathematical Society 8 Geometry & Topology 7 Publications Mathématiques 7 Proceedings of the Japan Academy. Series A 7 Journal of the Institute of Mathematics of Jussieu 6 Communications in Algebra 6 Journal of the London Mathematical Society. Second Series 6 Michigan Mathematical Journal 6 Oberwolfach Reports 5 Journal of the Mathematical Society of Japan 5 Proceedings of the American Mathematical Society 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 5 Electronic Research Archive 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Documenta Mathematica 4 Transformation Groups 4 Acta Mathematica Sinica. English Series 4 Kyoto Journal of Mathematics 4 Journal de l’École Polytechnique – Mathématiques 4 Peking Mathematical Journal 3 Russian Mathematical Surveys 3 Mathematische Nachrichten 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Experimental Mathematics 3 Taiwanese Journal of Mathematics 3 Milan Journal of Mathematics 3 Central European Journal of Mathematics 3 Forum of Mathematics, Pi 2 Communications on Pure and Applied Mathematics 2 Mathematical Notes 2 Acta Mathematica 2 Acta Mathematica Vietnamica 2 American Journal of Mathematics 2 Archiv der Mathematik 2 Bulletin of the London Mathematical Society 2 Collectanea Mathematica 2 Glasgow Mathematical Journal 2 Journal of Functional Analysis 2 Memoirs of the American Mathematical Society 2 Osaka Journal of Mathematics 2 Proceedings of the London Mathematical Society. Third Series 2 Bulletin of the Korean Mathematical Society 2 Revista Matemática Iberoamericana 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Sbornik: Mathematics 2 Izvestiya: Mathematics 2 Revista Matemática Complutense 2 Communications in Contemporary Mathematics 2 Journal of High Energy Physics 2 Advances in Geometry 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Science China. Mathematics 2 The Journal of Software for Algebra and Geometry 2 EMS Surveys in Mathematical Sciences 2 Complex Manifolds 2 Transactions of the American Mathematical Society. Series B 1 Journal of Mathematical Analysis and Applications 1 Nuclear Physics. B 1 Rocky Mountain Journal of Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Commentarii Mathematici Helvetici 1 Journal of Differential Geometry 1 Le Matematiche 1 Pacific Journal of Mathematics 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Tôhoku Mathematical Journal. Second Series 1 Publicacions Matemàtiques 1 Science in China. Series A 1 Sugaku Expositions 1 International Journal of Algebra and Computation ...and 20 more Serials all top 5 Cited in 27 Fields 616 Algebraic geometry (14-XX) 115 Several complex variables and analytic spaces (32-XX) 47 Differential geometry (53-XX) 36 Commutative algebra (13-XX) 19 Dynamical systems and ergodic theory (37-XX) 12 Group theory and generalizations (20-XX) 11 Nonassociative rings and algebras (17-XX) 10 Number theory (11-XX) 10 Associative rings and algebras (16-XX) 8 General and overarching topics; collections (00-XX) 8 General algebraic systems (08-XX) 5 History and biography (01-XX) 4 Category theory; homological algebra (18-XX) 4 Partial differential equations (35-XX) 3 Topological groups, Lie groups (22-XX) 3 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Quantum theory (81-XX) 2 Geometry (51-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Ordinary differential equations (34-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.