摘要翻译:
本文研究了维数$4G-3+n$的猜想族$x_{g,n}$上的Goulden-Jackson-Vakil公式的结构,该公式将Hurwitz数与某些猜想“交数”联系起来。我们给出了这些“交数”的适当排列的母函数的显式公式,并证明了它满足Hirota方程。这推广并实质上简化了我们在ARXIV:Math/0602457中用Zvonkine得到的早期结果。
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英文标题:
《On the structure of Goulden-Jackson-Vakil formula》
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作者:
S. Shadrin
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最新提交年份:
2008
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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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一级分类:Mathematics 数学
二级分类:Combinatorics 组合学
分类描述:Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学,图论,计数,组合优化,拉姆齐理论,组合对策论
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英文摘要:
We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural "intersection numbers" on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the properly arranged generating function for these "intersection numbers", and prove that it satisfies Hirota equations. This generalizes and substantially simplifies our earlier results with Zvonkine in arXiv:math/0602457.
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PDF链接:
https://arxiv.org/pdf/0810.0729