Toric变种中的实对数曲线、热带曲线和Log-Wellschinger不变量

Pub Date : 2020-04-10 DOI:10.5802/aif.3507
Hulya Arguz, Pierrick Bousseau
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引用次数: 3

摘要

给出了环面退化中实对数曲线计数的热带描述。我们讨论了零格曲线和所有非超丰富的高格情况。该证明依赖于对数变形理论,是对复杂曲线的热带对应定理的Nishinou-Siebert方法的一个真实版本。在二维空间中,我们用类似的方法研究了带有Welschinger符号的实对数曲线的计数,得到了关于Welschinger不变量的Mikhalkin热带对应定理的一个新的证明。
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Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants
We give a tropical description of the counting of real log curves in toric degenerations of toric varieties. We treat the case of genus zero curves and all non-superabundant higher-genus situations. The proof relies on log deformation theory and is a real version of the Nishinou-Siebert approach to the tropical correspondence theorem for complex curves. In dimension two, we use similar techniques to study the counting of real log curves with Welschinger signs and we obtain a new proof of Mikhalkin's tropical correspondence theorem for Welschinger invariants.
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