Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure

被引：0
|
作者：
Indranil Biswas
Ritwik Mukherjee
Varun Thakre
机构：
[1] Tata Institute of Fundamental Research,School of Mathematics
[2] National Institute of Science Education and Research,School of Mathematics
[3] Bhubaneswar (HBNI),undefined
[4] International Centre for Theoretical Sciences,undefined
来源：
Geometriae Dedicata | 2018年 / 195卷
关键词：
Genus two curves; Del-Pezzo surface; Symplectic invariant; Enumerative invariant; 53D45; 14N35; 14J45;
D O I：
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中图分类号：
学科分类号：
摘要：
We obtain a formula for the number of genus two curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This is done by extending the symplectic approach of Aleksey Zinger. This enumerative problem is expressed as the difference between the symplectic invariant and an intersection number on the moduli space of rational curves on the surface.
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页码：379 / 401
页数：22
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