×

zbMATH — the first resource for mathematics

The maximal number of quotient singularities on surfaces with given numerical invariants. (English) Zbl 0521.14013

MSC:
14J17 Singularities of surfaces or higher-dimensional varieties
57R20 Characteristic classes and numbers in differential topology
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14B05 Singularities in algebraic geometry
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] [Ba] Basset, A.B.: The maximum number of double points on a surface. Nature73, 246 (1906) · JFM 37.0646.03
[2] [Be] Beauville, A.: Sur le nombre maximum de points double d’une surface dansP 3 (?(5)=31). G?om?trie alg?brique d’Anger 1979, pp. 207-215. Alphen an den Rijn: Sijthoff & Nordohoff 1980
[3] [Br] Bruce, J.W.: An upper bound for the number of singularities on a projective hypersurface. Bull. Lond. Math. Soc.13, 47-51 (1981) · Zbl 0454.14018
[4] [CC] Catanese, F., Ceresa, G.: Constructing sextic surfaces with a given number of nodes. J. Pure Appl. Algebra23, 1-12 (1982) · Zbl 0484.14011
[5] [G] Gallarati, D.: Una superficie dell’ottavo ordine con 160 nodi. Acc. Ligure Sci. Lett.14, 1-7 (1957) · Zbl 0101.38604
[6] [Ka] Kawamata, Y.: On the classification of non-complete algebraic surfaces. Lecture Note in Mathematics, Vol. 732, pp. 215-232. Berlin, Heidelberg, New York: Springer 1979
[7] [Kr] Kreiss, H.O.: ?ber syzygetische Fl?chen. Ann. Math.41, 105-111 (1955)
[8] [M] Miyaoka, Y.: On the Chern numbers of surfaces of general type. Invert. Math.42, 225-237 (1977) · Zbl 0374.14007
[9] [N] Nikulin, V.V.: On Kummer surfaces. Math. USSR Izv.9, 261-275 (1975) · Zbl 0325.14015
[10] [Sa 1] Sakai, F.: Semi-stable curves on algebraic surfaces and logarithmic pluri-canonical maps. Math. Ann.254, 89-120 (1980) · Zbl 0437.14017
[11] [Sa2] Sakai, F.: Curves with trivial dualizing sheaf on algebraic surfaces. Am. J. Math.104, 1217-1231 (1982) · Zbl 0512.14021
[12] [Se1] Segre, B.: Sur massimo numero di nodi delle superficie di dato ordine. Bull. U.M.I.2, 204-212 (1947) · Zbl 0031.26201
[13] [Se2] Segre, B.: On arithmetical properties of quartic surfaces. Proc. London Math. Soc. 2nd Ser.49, 353-395 (1947) · Zbl 0034.08603
[14] [St1] Stagnaro, E.: Sul massimo numero di punti doppi isolati di una superficie algebrica diP 3. Rend. Sem. Nat. Padva59, 179-198 (1978) · Zbl 0427.14012
[15] [St2] Stagnaro, E.: On the Basset limitations for the maximum number of isolated singularities on an algebraic surface. Proc. of the Trento Conference, pp. 291-304. New York, Basel: Decker 1983
[16] [Y] Yau, S.T.: Calabi’s conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. USA74, 1798-1799 (1977) · Zbl 0355.32028
[17] [Z] Zariski, O.: The theorem of Rimann-Roch for high multiple of an effective divisor on a surface. Ann. Math.76, 506-615 (1962) · Zbl 0124.37001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.