摘要翻译:
我们证明了光滑代数簇X上的全纯双形$\theta$将稳定映射$\mgn(X,\beta)$模的虚基类局部化到$\theta$退化的轨迹;然后,我们可以定义局部GW不变量,它是辛几何中Lee和Parker局部不变量的代数几何模拟,当X为适当时,它与普通GW不变量是一致的。它是变形不变的。利用这一点,我们证明了Maulik和Pandharipande猜想的P_g>0的极小一般型曲面的低次GW-不变量的公式。
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英文标题:
《Gromov-Witten invariants of varieties with holomorphic 2-forms》
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作者:
Young-Hoon Kiem and Jun Li
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,\beta)$ to the locus where $\theta$ degenerates; it then enables us to define the localized GW-invariant, an algebro-geometric analogue of the local invariant of Lee and Parker in symplectic geometry, which coincides with the ordinary GW-invariant when X is proper. It is deformation invariant. Using this, we prove formulas for low degree GW-invariants of minimal general type surfaces with p_g>0 conjectured by Maulik and Pandharipande.
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PDF链接:
https://arxiv.org/pdf/0707.2986