Tohoku Mathematical Journal
2015
December
SECOND SERIES VOL. 67, NO. 4

Tohoku Math. J.
67 (2015), 585-609

Title THE SPECIAL MCKAY CORRESPONDENCE AND EXCEPTIONAL COLLECTIONS

Author Akira Ishii and Kazushi Ueda

(Received September 13, 2013)
Abstract. We show that the derived category of coherent sheaves on the quotient stack of the affine plane by a finite small subgroup of the general linear group is obtained from the derived category of coherent sheaves on the minimal resolution by adding a semiorthogonal summand with a full exceptional collection. The proof is based on an explicit construction in the abelian case, together with the analysis of the behavior of the derived categories of coherent sheaves under root constructions.

Mathematics Subject Classification. Primary 14E16; Secondary 14F05.
Key words and phrases. McKay correspondence, exceptional collections.

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