Duke Mathematical Journal

Matrix factorization of Morse–Bott functions

Constantin Teleman

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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.

Article information

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

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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

deformation theory supercategories matrix factorizations


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

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