科研之友
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摘要
Let S be a complex smooth projective surface and L be a line bundle on S. For any given collection of isolated topological or analytic singularity types, we show the number of curves in the linear system vertical bar L vertical bar with prescribed singularities is a universal polynomial of Chern numbers of L and S, assuming L is sufficiently ample. More generally, we show for vector bundles of any rank and smooth varieties of any dimension, similar universal polynomials also exist and equal the number of singular subvarieties cutting out by sections of the vector bundle. This work is a generalization of Gottsche's conjecture.
- 出版日期2014-7
