Journal article
Virtual Riemann-Roch theorems for almost perfect obstruction theories
Manuscripta mathematica, Vol.173(1-2), pp.463-498
01/01/2024
DOI: 10.1007/s00229-023-01458-7
Abstract
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-Gottsche 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.
Details
- Title: Subtitle
- Virtual Riemann-Roch theorems for almost perfect obstruction theories
- Creators
- Michail Savvas - The University of Texas at Austin
- Resource Type
- Journal article
- Publication Details
- Manuscripta mathematica, Vol.173(1-2), pp.463-498
- Publisher
- Springer Nature
- DOI
- 10.1007/s00229-023-01458-7
- ISSN
- 0025-2611
- eISSN
- 1432-1785
- Number of pages
- 36
- Language
- English
- Date published
- 01/01/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984696583502771
Metrics
1 Record Views