Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Threefold flops via matrix factorization


Authors: Carina Curto and David R. Morrison
Journal: J. Algebraic Geom. 22 (2013), 599-627
DOI: https://doi.org/10.1090/S1056-3911-2013-00633-5
Published electronically: April 2, 2013
MathSciNet review: 3084719
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Abstract | References | Additional Information

Abstract: The explicit McKay correspondence, as formulated by Gonzalez-
Sprinberg and Verdier, associates to each exceptional divisor in the minimal resolution of a rational double point, a matrix factorization of the equation of the rational double point. We study deformations of these matrix factorizations, and show that they exist over an appropriate ``partially resolved'' deformation space for rational double points of types A and D. As a consequence, all simple flops of lengths 1 and 2 can be described in terms of blowups defined from matrix factorizations. We also formulate conjectures which would extend these results to rational double points of type E and simple flops of length greater than 2.


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Additional Information

Carina Curto
Affiliation: Department of Mathematics, Box 90320, Duke University, Durham, North Carolina 27708
Address at time of publication: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588
Email: ccurto2@unl.edu

David R. Morrison
Affiliation: Department of Mathematics, Box 90320, Duke University, Durham North Carolina 27708
Address at time of publication: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: drm@math.ucsb.edu

DOI: https://doi.org/10.1090/S1056-3911-2013-00633-5
Received by editor(s): March 26, 2007
Received by editor(s) in revised form: September 3, 2008, and November 2, 2010
Published electronically: April 2, 2013
Additional Notes: The first author was supported by a National Science Foundation Graduate Research Fellowship and by National Science Foundation grant DMS-9983320; the second author was supported by National Science Foundation grants PHY-9907949 and DMS-0301476, the Clay Mathematics Foundation, the John Simon Guggenheim Memorial Foundation, the Kavli Institute for Theoretical Physics (Santa Barbara), and the Mathematical Sciences Research Institute (Berkeley) during the preparation of this paper. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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