Mathematics, Department of


Date of this Version



J. ALGEBRAIC GEOMETRY 22 (2013), pp. 599-627; S 1056-3911(2013)00633-5


Copyright 2013 University Press, Inc. Sponsored by the Department of Mathematical Sciences of Tsinghua University and distributed by the American Mathematical Society.


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.