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摘要翻译：
我们建立了量子最小Fano变体（关于Gromov-Witten理论的最小自然变体类）的0属Gromov-Witten不变量的抽象理论。特别地，我们考虑了“最小Gromov-Witten环”，即“最小Gromov-Witten环”。e.具有生成元和关系的交换代数，其形式为Fano簇的Gromov-Witten理论（维数不明）。任何量子极小变的Gromov-Witten理论都是这个环与$\MathBB C$的同态。我们证明了该环与由素两点不变量生成的自由交换环的特殊同构的抽象重构定理。用生成一个点Gromov-Witten不变量级数的方法，得到了N维Fano类的DN型微分方程的解。
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英文标题：
《Minimal Gromov--Witten ring》
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作者：
Victor Przyjalkowski
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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 build the abstract theory of Gromov-Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal natural (with respect to Gromov-Witten theory) class of varieties). In particular, we consider ``the minimal Gromov-Witten ring'', i. e. a commutative algebra with generators and relations of the form used in the Gromov-Witten theory of Fano variety (of unspecified dimension). Gromov-Witten theory of any quantum minimal variety is a homomorphism of this ring to $\mathbb C$. We prove the Abstract Reconstruction Theorem which states the particular isomorphism of this ring with a free commutative ring generated by ``prime two-pointed invariants''. We also find the solutions of the differential equations of type DN for a Fano variety of dimension N in terms of generating series of one-pointed Gromov-Witten invariants.
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PDF链接：
https://arxiv.org/pdf/0710.4084
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