Duke Mathematical Journal
- Duke Math. J.
- Volume 169, Number 3 (2020), 533-549.
Matrix factorization of Morse–Bott functions
For a function on a smooth algebraic variety with Morse–Bott critical locus , Kapustin, Rozansky, and Saulina suggest that the associated matrix factorization category should be equivalent to the differential graded category of -periodic coherent complexes on (with a topological twist from the normal bundle). We confirm their conjecture in the special case when the first neighborhood of in is split and establish the corrected general statement. The answer involves the full Gerstenhaber structure on Hochschild cochains. This note was inspired by the failure of the conjecture, observed by Pomerleano and Preygel, when is a general -parameter deformation of a surface .
Duke Math. J., Volume 169, Number 3 (2020), 533-549.
Received: 5 August 2017
Revised: 4 July 2019
First available in Project Euclid: 28 January 2020
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14B12: Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
Secondary: 14A10: Varieties and morphisms
Teleman, Constantin. Matrix factorization of Morse–Bott functions. Duke Math. J. 169 (2020), no. 3, 533--549. doi:10.1215/00127094-2019-0048. https://projecteuclid.org/euclid.dmj/1580202168