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15 February 2020 Matrix factorization of Morse–Bott functions
Constantin Teleman
Duke Math. J. 169(3): 533-549 (15 February 2020). DOI: 10.1215/00127094-2019-0048

Abstract

For a function WC[X] on a smooth algebraic variety X with Morse–Bott critical locus YX, Kapustin, Rozansky, and Saulina suggest that the associated matrix factorization category MF(X;W) should be equivalent to the differential graded category of 2-periodic coherent complexes on Y (with a topological twist from the normal bundle). We confirm their conjecture in the special case when the first neighborhood of Y in X 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 X is a general 1-parameter deformation of a K3 surface Y.

Citation

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Constantin Teleman. "Matrix factorization of Morse–Bott functions." Duke Math. J. 169 (3) 533 - 549, 15 February 2020. https://doi.org/10.1215/00127094-2019-0048

Information

Received: 5 August 2017; Revised: 4 July 2019; Published: 15 February 2020
First available in Project Euclid: 28 January 2020

zbMATH: 07198460
MathSciNet: MR4065148
Digital Object Identifier: 10.1215/00127094-2019-0048

Subjects:
Primary: 14B12
Secondary: 14A10

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 3 • 15 February 2020
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