A Gromov-Witten approach to $G$-equivariant birational invariants
| Autor: | Cavenaghi, Leonardo F., Grama, Lino, Katzarkov, Ludmil |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor invariants. Here, we rely on the profound geometric reasoning provided by Lupercio and Uribe in the early 00s to establish a connection between Chen-Ruan cohomology and several $G$-birational invariants introduced in the pioneering works Kontsevich, Kresch, Pestun, Tschinkel, along with presenting applications. Combined with the theory of atoms by Katzarkov, Kontsevich, Pantev, and Yu, the proposal in this paper program will lead to a theory of equivariant atoms. Comment: a) Clarified what kind of group actions we are considering. b) Recalled birationality for Deligne-Mumford (DM) stacks and explained how they still contain information on finite group actions. c) Explained the role of gerbes in twisting Chen-Ruan cohomology and presented details on how they can be useful in obstructing birational types of certain DM stacks. 32 pages. 1 Appendix |
| Databáze: | arXiv |
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