热带曲线与代数曲线之间的亏格一对应
Genus one correspondence between tropical and algebraic curves
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中文总结 AI 辅助
研究热带曲线与代数曲线的亏格一对应，通过对数形变理论及固定热带化的对数映射枚举，证明代数椭圆曲线计数与热带曲线计数一致，推广了亏格0的对应定理。
中文摘要 AI 辅助
我们证明，在任何环面簇中，代数椭圆曲线的真正枚举计数与相应的间隔良好的热带曲线的计数一致，并由明确的组合重数加权。这提供了亏格0中著名的西野-西伯特对应定理的完整亏格1推广。证明是代数几何的，依赖于对数形变理论以及对具有固定热带化的对数映射的明确枚举。
英文摘要
We show that the genuinely enumerative count of algebraic elliptic curves in any toric variety agrees with the count of the corresponding well-spaced tropical curves, weighted by explicit combinatorial multiplicities. This provides a complete genus-$1$ generalization of the celebrated Nishinou--Siebert correspondence theorem in genus $0$. The proof is algebro-geometric and relies on logarithmic deformation theory together with an explicit enumeration of logarithmic maps with fixed tropicalization.
