Journal article
Localizing virtual structure sheaves for almost perfect obstruction theories
Forum of mathematics. Sigma, Vol.8, e61
2020
DOI: 10.1017/fms.2020.59
Abstract
Almost perfect obstruction theories were introduced in an earlier paper by the authors as the appropriate notion in order to define virtual structure sheaves and K-theoretic invariants for many moduli stacks of interest, including K-theoretic Donaldson-Thomas invariants of sheaves and complexes on Calabi-Yau threefolds. The construction of virtual structure sheaves is based on the K-theory and Gysin maps of sheaf stacks.
In this paper, we generalize the virtual torus localization and cosection localization formulas and their combination to the setting of almost perfect obstruction theory. To this end, we further investigate the K-theory of sheaf stacks and its functoriality properties. As applications of the localization formulas, we establish a K-theoretic wall-crossing formula for simple
$\mathbb{C} ^\ast $
-wall crossings and define K-theoretic invariants refining the Jiang-Thomas virtual signed Euler characteristics.
Details
- Title: Subtitle
- Localizing virtual structure sheaves for almost perfect obstruction theories
- Creators
- Young-Hoon KiemMichail Savvas - University of California San Diego
- Resource Type
- Journal article
- Publication Details
- Forum of mathematics. Sigma, Vol.8, e61
- DOI
- 10.1017/fms.2020.59
- ISSN
- 2050-5094
- eISSN
- 2050-5094
- Publisher
- Cambridge University Press
- Number of pages
- 36
- Language
- English
- Date published
- 2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984696582902771
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