Virtual Riemann-Roch Theorems for Almost Perfect Obstruction Theories
| Autor: | Savvas, Michail |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00229-023-01458-7 |
| Popis: | This is the third in a series of works devoted to constructing virtual structure sheaves and $K$-theoretic invariants in moduli theory. The central objects of study are almost perfect obstruction theories, introduced by Y.-H. Kiem and the author as the appropriate notion in order to define invariants in $K$-theory for many moduli stacks of interest, including generalized $K$-theoretic Donaldson-Thomas invariants. In this paper, we prove virtual Riemann-Roch theorems in the setting of almost perfect obstruction theory in both the non-equivariant and equivariant cases, including cosection localized versions. These generalize and remove technical assumptions from the virtual Riemann-Roch theorems of Fantechi-G\"{o}ttsche and Ravi-Sreedhar. The main technical ingredients are a treatment of the equivariant $K$-theory and equivariant Gysin map of sheaf stacks and a formula for the virtual Todd class. Comment: 33 pages; added application, improved exposition. Published version |
| Databáze: | arXiv |
| Externí odkaz: |
|