COUNTING RATIONAL CURVES ON K3 SURFACES
作者： Arnaud Beauville
DOI: 10.1215/S0012-7094-99-09704-1
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摘要: The aim of these notes is to explain the remarkable formula found by Yau and Zaslow [Y-Z] express number rational curves on a K3 surface. Projective surfaces fall into countably many families (Fg)g≥1 ; surface in Fg admits gdimensional linear system genus g . A naive count constants suggests that such will contain positive number, say n(g) , (highly singular) curves. is∑
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arxiv.org 参考文章(11)
Duco van Straten, Lothar Göttsche, Barbara Fantechi, Euler number of the compactified Jacobian and multiplicity of rational curves arXiv: Algebraic Geometry. ,(1997)
Lothar Göttsche, The Betti numbers of the Hilbert scheme of points on a smooth projective surface Mathematische Annalen. ,vol. 286, pp. 193- 207 ,(1990) , 10.1007/BF01453572
Daniel Huybrechts, Compact hyperkähler manifolds: basic results Inventiones Mathematicae. ,vol. 135, pp. 63- 113 ,(1999) , 10.1007/S00222-002-0280-5
Jean-Louis Verdier, Stratifications de Whitney et théorème de Bertini-Sard Inventiones Mathematicae. ,vol. 36, pp. 295- 312 ,(1976) , 10.1007/BF01390015
G. -M. Greuel, H. Kn�rrer, Einfache Kurvensingularitäten und torsionsfreie Moduln Mathematische Annalen. ,vol. 270, pp. 417- 425 ,(1985) , 10.1007/BF01473437
Shigeru Mukai, Symplectic structure of the moduli space of sheaves on an abelian or K3 surface. Inventiones Mathematicae. ,vol. 77, pp. 101- 116 ,(1984) , 10.1007/BF01389137
A. Bialynicki-Birula, On fixed point schemes of actions of multiplicative and additive groups Topology. ,vol. 12, pp. 99- 103 ,(1973) , 10.1016/0040-9383(73)90024-4
Shing-Tung Yau, Eric Zaslow, BPS states, string duality, and nodal curves on K3 Nuclear Physics. ,vol. 471, pp. 503- 512 ,(1996) , 10.1016/0550-3213(96)00176-9
Victor V. Batyrev, On the Betti numbers of birationally isomorphic projective varieties with trivial canonical bundles ,(1997)
C. J. Rego, The compactified Jacobian Annales Scientifiques De L Ecole Normale Superieure. ,vol. 13, pp. 211- 223 ,(1980) , 10.24033/ASENS.1380