Averkov, Gennadiy; Hofscheier, Johannes; Nill, Benjamin Generalized flatness constants, spanning lattice polytopes, and the Gromov width. (English) Zbl 1508.52006 Manuscr. Math. 170, No. 1-2, 147-165 (2023). MSC: 52B20 53D05 14M25 PDFBibTeX XMLCite \textit{G. Averkov} et al., Manuscr. Math. 170, No. 1--2, 147--165 (2023; Zbl 1508.52006) Full Text: DOI arXiv
Kasprzyk, Alexander M. (ed.); Nill, Benjamin (ed.) Interactions with lattice polytopes. Selected papers based on the presentations at the workshop, Magdeburg, Germany, September 14–16, 2017. (English) Zbl 1497.52003 Springer Proceedings in Mathematics & Statistics 386. Cham: Springer (ISBN 978-3-030-98326-0/hbk; 978-3-030-98327-7/ebook). x, 364 p. (2022). MSC: 52-06 14-06 13-06 52B20 14M25 13F55 13F65 PDFBibTeX XMLCite \textit{A. M. Kasprzyk} (ed.) and \textit{B. Nill} (ed.), Interactions with lattice polytopes. Selected papers based on the presentations at the workshop, Magdeburg, Germany, September 14--16, 2017. Cham: Springer (2022; Zbl 1497.52003) Full Text: DOI
Hering, Milena; Nill, Benjamin; Süß, Hendrik Stability of tangent bundles on smooth toric Picard-rank-\(2\) varieties and surfaces. (English) Zbl 1489.14065 Aluffi, Paolo (ed.) et al., Facets of algebraic geometry. A collection in honor of William Fulton’s 80th birthday. Volume 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 473, 1-25 (2022). MSC: 14M25 14J60 PDFBibTeX XMLCite \textit{M. Hering} et al., Lond. Math. Soc. Lect. Note Ser. 473, 1--25 (2022; Zbl 1489.14065) Full Text: DOI arXiv
Averkov, Gennadiy; Kasprzyk, Alexander; Lehmann, Martin; Nill, Benjamin Sharp bounds on fake weighted projective spaces with canonical singularities. arXiv:2105.09635 Preprint, arXiv:2105.09635 [math.AG] (2021). MSC: 14M25 52B20 BibTeX Cite \textit{G. Averkov} et al., ``Sharp bounds on fake weighted projective spaces with canonical singularities'', Preprint, arXiv:2105.09635 [math.AG] (2021) Full Text: arXiv OA License
Borger, Christopher; Nill, Benjamin On defectivity of families of full-dimensional point configurations. (English) Zbl 1442.14164 Proc. Am. Math. Soc., Ser. B 7, 43-51 (2020). MSC: 14M25 52B20 52A39 13P15 PDFBibTeX XMLCite \textit{C. Borger} and \textit{B. Nill}, Proc. Am. Math. Soc., Ser. B 7, 43--51 (2020; Zbl 1442.14164) Full Text: DOI arXiv
Di Rocco, Sandra; Haase, Christian; Nill, Benjamin A note on discrete mixed volume and Hodge-Deligne numbers. (English) Zbl 1409.14084 Adv. Appl. Math. 104, 1-13 (2019). MSC: 14M25 14M10 52B20 PDFBibTeX XMLCite \textit{S. Di Rocco} et al., Adv. Appl. Math. 104, 1--13 (2019; Zbl 1409.14084) Full Text: DOI arXiv
Hofscheier, Johannes; Nill, Benjamin; Öberg, Dennis On Ehrhart polynomials of lattice triangles. (English) Zbl 1386.52012 Electron. J. Comb. 25, No. 1, Research Paper P1.3, 8 p. (2018). MSC: 52B20 52C05 14M25 PDFBibTeX XMLCite \textit{J. Hofscheier} et al., Electron. J. Comb. 25, No. 1, Research Paper P1.3, 8 p. (2018; Zbl 1386.52012) Full Text: arXiv Link
Kasprzyk, Alexander; Nill, Benjamin; Prince, Thomas Minimality and mutation-equivalence of polygons. (English) Zbl 1394.14034 Forum Math. Sigma 5, Paper No. e18, 48 p. (2017). Reviewer: Andrea Petracci (Nottingham) MSC: 14M25 52B20 14J45 14J26 14J33 PDFBibTeX XMLCite \textit{A. Kasprzyk} et al., Forum Math. Sigma 5, Paper No. e18, 48 p. (2017; Zbl 1394.14034) Full Text: DOI arXiv
Assarf, Benjamin; Nill, Benjamin A bound for the splitting of smooth Fano polytopes with many vertices. (English) Zbl 1333.52015 J. Algebr. Comb. 43, No. 1, 153-172 (2016). MSC: 52B20 14M25 14J45 PDFBibTeX XMLCite \textit{B. Assarf} and \textit{B. Nill}, J. Algebr. Comb. 43, No. 1, 153--172 (2016; Zbl 1333.52015) Full Text: DOI arXiv
Balletti, Gabriele; Kasprzyk, Alexander M.; Nill, Benjamin On the maximum dual volume of a canonical Fano polytope. arXiv:1611.02455 Preprint, arXiv:1611.02455 [math.CO] (2016). MSC: 52B20 14M25 BibTeX Cite \textit{G. Balletti} et al., ``On the maximum dual volume of a canonical Fano polytope'', Preprint, arXiv:1611.02455 [math.CO] (2016) Full Text: arXiv OA License
Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin Largest integral simplices with one interior integral point: solution of Hensley’s conjecture and related results. (English) Zbl 1378.52014 Adv. Math. 274, 118-166 (2015). Reviewer: Edwin León Cardenal (Zacatecas) MSC: 52B20 52B12 52A38 14M25 90C11 PDFBibTeX XMLCite \textit{G. Averkov} et al., Adv. Math. 274, 118--166 (2015; Zbl 1378.52014) Full Text: DOI arXiv
Lorenz, Benjamin; Nill, Benjamin On smooth Gorenstein polytopes. (English) Zbl 1338.52014 Tohoku Math. J. (2) 67, No. 4, 513-530 (2015). Reviewer: Matthias Beck (San Francisco) MSC: 52B20 14M25 14J45 PDFBibTeX XMLCite \textit{B. Lorenz} and \textit{B. Nill}, Tôhoku Math. J. (2) 67, No. 4, 513--530 (2015; Zbl 1338.52014) Full Text: DOI arXiv Euclid
Bogart, Tristram; Haase, Christian; Hering, Milena; Lorenz, Benjamin; Nill, Benjamin; Paffenholz, Andreas; Rote, Günter; Santos, Francisco; Schenck, Hal Finitely many smooth \(d\)-polytopes with \(n\) lattice points. (English) Zbl 1327.52020 Isr. J. Math. 207, Part 1, 301-329 (2015). Reviewer: Ignacio García Marco (Lyon) MSC: 52B20 14M25 PDFBibTeX XMLCite \textit{T. Bogart} et al., Isr. J. Math. 207, Part 1, 301--329 (2015; Zbl 1327.52020) Full Text: DOI arXiv
Baumeister, Barbara; Haase, Christian; Nill, Benjamin Polytopes associated to dihedral groups. (English) Zbl 1336.52016 Ars Math. Contemp. 7, No. 1, 30-38 (2014). MSC: 52B15 52B12 05C10 52B05 52B20 20B35 PDFBibTeX XMLCite \textit{B. Baumeister} et al., Ars Math. Contemp. 7, No. 1, 30--38 (2014; Zbl 1336.52016) Full Text: DOI arXiv
Di Rocco, Sandra; Haase, Christian; Nill, Benjamin; Paffenholz, Andreas Polyhedral adjunction theory. (English) Zbl 1333.14010 Algebra Number Theory 7, No. 10, 2417-2446 (2013). Reviewer: Christos Tatakis (Mitilini) MSC: 14C20 14M25 52B20 PDFBibTeX XMLCite \textit{S. Di Rocco} et al., Algebra Number Theory 7, No. 10, 2417--2446 (2013; Zbl 1333.14010) Full Text: DOI arXiv
Nill, Benjamin; Schepers, Jan Gorenstein polytopes and their stringy \(E\)-functions. (English) Zbl 1271.14076 Math. Ann. 355, No. 2, 457-480 (2013). Reviewer: Serge Lawrencenko (Moskva) MSC: 14M25 52B20 14J32 PDFBibTeX XMLCite \textit{B. Nill} and \textit{J. Schepers}, Math. Ann. 355, No. 2, 457--480 (2013; Zbl 1271.14076) Full Text: DOI arXiv
Baumeister, Barbara; Haase, Christian; Nill, Benjamin; Paffenholz, Andreas Permutation polytopes of cyclic groups. (English. French summary) Zbl 1417.52012 Proceedings of the 24th international conference on formal power series and algebraic combinatorics, FPSAC 2012, Nagoya, Japan, July 30–August 3, 2012. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Math. Theor. Comput. Sci., Proc., 421-432 (2012). MSC: 52B05 PDFBibTeX XMLCite \textit{B. Baumeister} et al., in: Proceedings of the 24th international conference on formal power series and algebraic combinatorics, FPSAC 2012, Nagoya, Japan, July 30--August 3, 2012. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). 421--432 (2012; Zbl 1417.52012) Full Text: arXiv Link
Kasprzyk, Alexander M.; Nill, Benjamin Reflexive polytopes of higher index and the number 12. (English) Zbl 1258.52008 Electron. J. Comb. 19, No. 3, Research Paper P9, 18 p. (2012). MSC: 52B20 14M25 14Q10 PDFBibTeX XMLCite \textit{A. M. Kasprzyk} and \textit{B. Nill}, Electron. J. Comb. 19, No. 3, Research Paper P9, 18 p. (2012; Zbl 1258.52008) Full Text: arXiv Link
Dickenstein, Alicia; Nill, Benjamin; Vergne, Michèle A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes. (English. French summary) Zbl 1251.52007 C. R., Math., Acad. Sci. Paris 350, No. 5-6, 229-233 (2012). Reviewer: Oleg Karpenkov (Graz) MSC: 52B20 14M25 PDFBibTeX XMLCite \textit{A. Dickenstein} et al., C. R., Math., Acad. Sci. Paris 350, No. 5--6, 229--233 (2012; Zbl 1251.52007) Full Text: DOI arXiv
Nill, Benjamin; Paffenholz, Andreas Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes. (English) Zbl 1225.14042 Beitr. Algebra Geom. 52, No. 2, 297-304 (2011). Reviewer: G. K. Sankaran (Bath) MSC: 14M25 14J45 32Q20 52B20 53C25 PDFBibTeX XMLCite \textit{B. Nill} and \textit{A. Paffenholz}, Beitr. Algebra Geom. 52, No. 2, 297--304 (2011; Zbl 1225.14042) Full Text: DOI arXiv
Kasprzyk, Alexander M.; Kreuzer, Maximilian; Nill, Benjamin On the combinatorial classification of toric log del Pezzo surfaces. (English) Zbl 1230.14077 LMS J. Comput. Math. 13, 33-46 (2010). Reviewer: Anargyros Katsabekis (Lamia) MSC: 14M25 14J26 52B20 PDFBibTeX XMLCite \textit{A. M. Kasprzyk} et al., LMS J. Comput. Math. 13, 33--46 (2010; Zbl 1230.14077) Full Text: DOI arXiv
Dickenstein, Alicia; Nill, Benjamin A simple combinatorial criterion for projective toric manifolds with dual defect. (English) Zbl 1243.52010 Math. Res. Lett. 17, No. 3, 435-448 (2010). MSC: 52B20 14M25 PDFBibTeX XMLCite \textit{A. Dickenstein} and \textit{B. Nill}, Math. Res. Lett. 17, No. 3, 435--448 (2010; Zbl 1243.52010) Full Text: DOI arXiv
Nill, Benjamin; Øbro, Mikkel \(Q\)-factorial Gorenstein toric Fano varieties with large Picard number. (English) Zbl 1211.14048 Tohoku Math. J. (2) 62, No. 1, 1-15 (2010). Reviewer: Victor Przyjalkowski (Moskva) MSC: 14J45 52B20 14M25 PDFBibTeX XMLCite \textit{B. Nill} and \textit{M. Øbro}, Tôhoku Math. J. (2) 62, No. 1, 1--15 (2010; Zbl 1211.14048) Full Text: DOI arXiv
Haase, Christian; Nill, Benjamin; Payne, Sam Cayley decompositions of lattice polytopes and upper bounds for \(h^ *\)-polynomials. (English) Zbl 1185.52012 J. Reine Angew. Math. 637, 207-216 (2009). Reviewer: Matthias Beck (San Francisco) MSC: 52B20 05A15 14M25 52C07 PDFBibTeX XMLCite \textit{C. Haase} et al., J. Reine Angew. Math. 637, 207--216 (2009; Zbl 1185.52012) Full Text: DOI arXiv
Altmann, Klaus; Nill, Benjamin; Schwentner, Sabine; Wiercinska, Izolda Flow polytopes and the graph of reflexive polytopes. (English) Zbl 1207.52014 Discrete Math. 309, No. 16, 4992-4999 (2009). Reviewer: James F. Lawrence (Fairfax) MSC: 52B20 14M25 PDFBibTeX XMLCite \textit{K. Altmann} et al., Discrete Math. 309, No. 16, 4992--4999 (2009; Zbl 1207.52014) Full Text: DOI
Baumeister, Barbara; Haase, Christian; Nill, Benjamin; Paffenholz, Andreas On permutation polytopes. (English) Zbl 1185.52006 Adv. Math. 222, No. 2, 431-452 (2009). Reviewer: Matthias Beck (San Francisco) MSC: 52B05 05A05 15A15 52B12 PDFBibTeX XMLCite \textit{B. Baumeister} et al., Adv. Math. 222, No. 2, 431--452 (2009; Zbl 1185.52006) Full Text: DOI arXiv
Kreuzer, Maximilian; Nill, Benjamin Classification of toric Fano 5-folds. (English) Zbl 1193.14067 Adv. Geom. 9, No. 1, 85-97 (2009). Reviewer: Gianluca Occhetta (Trento) MSC: 14M25 14J45 14J40 PDFBibTeX XMLCite \textit{M. Kreuzer} and \textit{B. Nill}, Adv. Geom. 9, No. 1, 85--97 (2009; Zbl 1193.14067) Full Text: DOI arXiv
Haase, Christian; Nill, Benjamin; Paffenholz, Andreas; Santos, Francisco Lattice points in Minkowski sums. (English) Zbl 1160.52009 Electron. J. Comb. 15, No. 1, Research Paper N11, 5 p. (2008). MSC: 52B20 14M25 PDFBibTeX XMLCite \textit{C. Haase} et al., Electron. J. Comb. 15, No. 1, Research Paper N11, 5 p. (2008; Zbl 1160.52009) Full Text: arXiv EuDML EMIS
Batyrev, Victor; Nill, Benjamin Combinatorial aspects of mirror symmetry. (English) Zbl 1161.14037 Beck, Matthias (ed.) et al., Integer points in polyhedra—geometry, number theory, algebra, optimization, statistics. Proceedings of the AMS-IMS-SIAM joint summer research conference, Snowbird, UT, USA, June 11–15, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4173-0/pbk). Contemporary Mathematics 452, 35-66 (2008). Reviewer: Oleg Karpenkov (Graz) MSC: 14M25 14J32 52B20 PDFBibTeX XMLCite \textit{V. Batyrev} and \textit{B. Nill}, Contemp. Math. 452, 35--66 (2008; Zbl 1161.14037) Full Text: arXiv
Dais, Dimitrios I.; Nill, Benjamin A boundedness result for toric log del Pezzo surfaces. (English) Zbl 1156.14040 Arch. Math. 91, No. 6, 526-535 (2008). Reviewer: Amanda Knecht (Ann Arbor) MSC: 14M25 14J26 14Q10 52B20 PDFBibTeX XMLCite \textit{D. I. Dais} and \textit{B. Nill}, Arch. Math. 91, No. 6, 526--535 (2008; Zbl 1156.14040) Full Text: DOI arXiv
Haase, Christian; Nill, Benjamin Lattices generated by skeletons of reflexive polytopes. (English) Zbl 1138.14033 J. Comb. Theory, Ser. A 115, No. 2, 340-344 (2008). Reviewer: Parameswaran Sankaran (Chennai) MSC: 14M25 52B20 PDFBibTeX XMLCite \textit{C. Haase} and \textit{B. Nill}, J. Comb. Theory, Ser. A 115, No. 2, 340--344 (2008; Zbl 1138.14033) Full Text: DOI arXiv
Batyrev, Victor; Nill, Benjamin Multiples of lattice polytopes without interior lattice points. (English) Zbl 1134.52020 Mosc. Math. J. 7, No. 2, 195-207 (2007). Reviewer: Volker Kaibel (Magdeburg) MSC: 52B20 14M25 PDFBibTeX XMLCite \textit{V. Batyrev} and \textit{B. Nill}, Mosc. Math. J. 7, No. 2, 195--207 (2007; Zbl 1134.52020) Full Text: arXiv
Nill, Benjamin Volume and lattice points of reflexive simplices. (English) Zbl 1166.52013 Discrete Comput. Geom. 37, No. 2, 301-320 (2007). MSC: 52B20 14M25 11D68 PDFBibTeX XMLCite \textit{B. Nill}, Discrete Comput. Geom. 37, No. 2, 301--320 (2007; Zbl 1166.52013) Full Text: DOI arXiv
Nill, Benjamin Classification of pseudo-symmetric simplicial reflexive polytopes. (English) Zbl 1126.52013 Athanasiadis, Christos A. (ed.) et al., Algebraic and geometric combinatorics. Euroconference in mathematics, algebraic and geometric combinatorics, Anogia, Crete, Greece, August 20–26, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-4080-0/pbk). Contemporary Mathematics 423, 269-282 (2006). Reviewer: Egon Schulte (Boston) MSC: 52B20 14M25 14J45 52B12 PDFBibTeX XMLCite \textit{B. Nill}, Contemp. Math. 423, 269--282 (2006; Zbl 1126.52013) Full Text: arXiv
Nill, Benjamin Complete toric varieties with reductive automorphism group. (English) Zbl 1091.14011 Math. Z. 252, No. 4, 767-786 (2006). Reviewer: Dmitri Panyushev (Moskva) MSC: 14J50 14M25 14J45 52B20 PDFBibTeX XMLCite \textit{B. Nill}, Math. Z. 252, No. 4, 767--786 (2006; Zbl 1091.14011) Full Text: DOI arXiv
Nill, Benjamin Gorenstein toric Fano varieties. (English) Zbl 1067.14052 Manuscr. Math. 116, No. 2, 183-210 (2005). Reviewer: G. K. Sankaran (Bath) MSC: 14M25 14J45 52B20 PDFBibTeX XMLCite \textit{B. Nill}, Manuscr. Math. 116, No. 2, 183--210 (2005; Zbl 1067.14052) Full Text: DOI arXiv