Journal article
K-Theoretic Generalized Donaldson-Thomas Invariants
International mathematics research notices, Vol.2021(24), pp.19055-19090
02/01/2022
DOI: 10.1093/imrn/rnaa097
Abstract
We introduce the notion of almost perfect obstruction theory on a Deligne-Mumford stack and show that stacks with almost perfect obstruction theories have virtual structure sheaves, which are deformation invariant. The main components in the construction are an induced embedding of the coarse moduli sheaf of the intrinsic normal cone into the associated obstruction sheaf stack and the construction of a K-theoretic Gysinmap for sheaf stacks. We show that many stacks of interest admit almost perfect obstruction theories. As a result, we are able to define virtual structure sheaves and K-theoretic classical and generalized Donaldson-Thomas invariants of sheaves and complexes on Calabi-Yau three-folds.
Details
- Title: Subtitle
- K-Theoretic Generalized Donaldson-Thomas Invariants
- Creators
- Young-Hoon Kiem - Seoul Natl Univ, Dept Math Sci, Seoul 08826, South KoreaMichail Savvas - University of California, San Diego
- Resource Type
- Journal article
- Publication Details
- International mathematics research notices, Vol.2021(24), pp.19055-19090
- Publisher
- Oxford Univ Press
- DOI
- 10.1093/imrn/rnaa097
- ISSN
- 1073-7928
- eISSN
- 1687-0247
- Number of pages
- 36
- Grant note
- SSTF-BA1601-01 / Samsung Science and Technology Foundation; Samsung
- Language
- English
- Date published
- 02/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984696715602771
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