{"title":"定向实有理曲线的精细化计数","authors":"Thomas Blomme","doi":"10.1090/jag/801","DOIUrl":null,"url":null,"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 \n\n \n 2\n 2\n \n\n-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.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Refined count of oriented real rational curves\",\"authors\":\"Thomas Blomme\",\"doi\":\"10.1090/jag/801\",\"DOIUrl\":null,\"url\":null,\"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 \\n\\n \\n 2\\n 2\\n \\n\\n-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.\",\"PeriodicalId\":54887,\"journal\":{\"name\":\"Journal of Algebraic Geometry\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/jag/801\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jag/801","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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