摘要翻译:
如果一条曲线可以用相对于它的牛顿多面体非退化的洛朗多项式来建模,那么它就被称为非退化曲线。我们证明了直到亏格4,每条曲线都是非退化的。我们还证明了固定亏格g>1的曲线模空间内的非退化曲线的轨迹是min(2g+1,3G-3)维的,但在g=7的情况下是16维的除外。
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英文标题:
《On nondegeneracy of curves》
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作者:
Wouter Castryck, John Voight
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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:
A curve is called nondegenerate if it can be modeled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We show that up to genus 4, every curve is nondegenerate. We also prove that the locus of nondegenerate curves inside the moduli space of curves of fixed genus g > 1 is min(2g+1,3g-3)-dimensional, except in case g=7 where it is 16-dimensional.
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PDF链接:
https://arxiv.org/pdf/0802.0420