Towards logarithmic GLSM: the r-spin case

被引:1
作者
Chen, Qile [1 ,5 ]
Janda, Felix [2 ]
Ruan, Yongbin [3 ]
Sauvaget, Adrien [4 ]
机构
[1] Boston Coll, Dept Math, Chestnut Hill, MA 02467 USA
[2] Univ Notre Dame, Dept Math, Notre Dame, IN USA
[3] Zhejiang Univ, Adv Study Math, Hangzhou, Peoples R China
[4] Univ Paris 06, Inst Math Jussieu, Paris, France
[5] Univ Cergy Pontoise, CNRS, Lab Math AGM, UMR 8088, Cergy, France
基金
美国国家科学基金会;
关键词
GROMOV-WITTEN INVARIANTS; TAUTOLOGICAL RELATIONS; VIRTUAL CYCLES; MODULI; GEOMETRY; CURVES; LOCALIZATION; MORPHISMS; FORMULA; SPACE;
D O I
10.2140/gt.2022.26.2855
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We establish the logarithmic foundation for compactifying the moduli stacks of the gauged linear sigma model using stable log maps. We then illustrate our method via the key example of Witten's r-spin class to construct a proper moduli stack with a reduced perfect obstruction theory whose virtual cycle recovers the r-spin virtual cycle of Chang, Li and Li. Indeed, our construction of the reduced virtual cycle is built upon their work by appropriately extending and modifying the Kiem-Li cosection along certain logarithmic boundary. In a follow-up article, we push the technique to a general situation. One motivation of our construction is to fit the gauged linear sigma model in the broader setting of Gromov-Witten theory so that powerful tools such as virtual localization can be applied. A project along this line is currently in progress, leading to applications including computing loci of holomorphic differentials, and calculating Gromov-Witten invariants of threefolds.
引用
收藏
页码:2855 / 2939
页数:86
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