Refined count of oriented real rational curves

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2023-05-05 DOI:10.1090/jag/801

Thomas Blomme

引用次数: 0

Abstract

We introduce a quantum index for oriented real curves inside toric varieties. This quantum index is related to the computation of the area of the amoeba of the curve for some chosen 2 2 -form. We then make a refined signed count of oriented real rational curves solution to some enumerative problem. This generalizes the 2017 results of Mikhalkin to higher dimension. Finally, we use the tropical approach to relate these new refined invariants to previously known tropical refined invariants.

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定向实有理曲线的精细化计数

我们引入了复曲面内有向实曲线的量子指数。这个量子指数与某些选定的2-2形式的曲线变形虫面积的计算有关。然后，我们对一些枚举问题给出了一个有向实有理曲线的精细有符号计数解。这将Mikhalkin 2017年的结果推广到了更高的维度。最后，我们使用热带方法将这些新的精化不变量与以前已知的热带精化不变量联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.