{"title":"实数曲面上典型次为2的实数有理曲线的组合计数","authors":"S. Finashin, V. Kharlamov","doi":"10.1017/s1474748022000317","DOIUrl":null,"url":null,"abstract":"\n We propose two systems of “intrinsic” weights for counting such curves. In both cases the result acquires an exceptionally strong invariance property: it does not depend on the choice of a surface. One of our counts includes all divisor classes of canonical degree 2 and gives in total 30. The other one excludes the class \n \n \n \n$-2K$\n\n \n , but adds up the results of counting for a pair of real structures that differ by Bertini involution. This count gives 96.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"COMBINED COUNT OF REAL RATIONAL CURVES OF CANONICAL DEGREE 2 ON REAL DEL PEZZO SURFACES WITH\",\"authors\":\"S. Finashin, V. Kharlamov\",\"doi\":\"10.1017/s1474748022000317\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n We propose two systems of “intrinsic” weights for counting such curves. In both cases the result acquires an exceptionally strong invariance property: it does not depend on the choice of a surface. One of our counts includes all divisor classes of canonical degree 2 and gives in total 30. The other one excludes the class \\n \\n \\n \\n$-2K$\\n\\n \\n , but adds up the results of counting for a pair of real structures that differ by Bertini involution. This count gives 96.\",\"PeriodicalId\":50002,\"journal\":{\"name\":\"Journal of the Institute of Mathematics of Jussieu\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Institute of Mathematics of Jussieu\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s1474748022000317\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1474748022000317","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
COMBINED COUNT OF REAL RATIONAL CURVES OF CANONICAL DEGREE 2 ON REAL DEL PEZZO SURFACES WITH
We propose two systems of “intrinsic” weights for counting such curves. In both cases the result acquires an exceptionally strong invariance property: it does not depend on the choice of a surface. One of our counts includes all divisor classes of canonical degree 2 and gives in total 30. The other one excludes the class
$-2K$
, but adds up the results of counting for a pair of real structures that differ by Bertini involution. This count gives 96.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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