{"title":"Tropical curves in abelian surfaces I: enumeration of curves passing through points","authors":"THOMAS BLOMME","doi":"10.1017/s0305004124000161","DOIUrl":null,"url":null,"abstract":"<p>This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we consider the enumeration of genus <span>g</span> curves of fixed degree passing through <span>g</span> points. We compute the tropical multiplicity provided by a correspondence theorem due to T. Nishinou and show that it is possible to refine this multiplicity in the style of the Block–Göttsche refined multiplicity to get tropical refined invariants.</p>","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"2 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Cambridge Philosophical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0305004124000161","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we consider the enumeration of genus g curves of fixed degree passing through g points. We compute the tropical multiplicity provided by a correspondence theorem due to T. Nishinou and show that it is possible to refine this multiplicity in the style of the Block–Göttsche refined multiplicity to get tropical refined invariants.
本文是通过热带方法研究无性曲面枚举不变式的系列论文的第一部分。在本文中，我们考虑枚举通过 g 个点的固定阶数的 g 属曲线。我们计算了由 T. Nishinou 提出的对应定理所提供的热带多重性，并证明可以按照 Block-Göttsche 精炼多重性的方式对这一多重性进行精炼，从而得到热带精炼不变式。
期刊介绍：
Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.
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