Pure and Applied Mathematics Quarterly
Volume 11 (2015)
$K$-theoretic and categorical properties of toric Deligne–Mumford stacks
Pages: 239 – 266
We prove the following results for toric Deligne–Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant $K$-theory; the equivariant Hirzebruch–Riemann–Roch theorem; the Fourier–Mukai transformation associated to a crepant toric wall-crossing gives an equivariant derived equivalence.
toric Deligne–Mumford stacks, orbifolds, $K$-theory, localization, derived category of coherent sheaves, Fourier–Mukai transformation, flop, $K$-equivalence, equivariant, variation of GIT quotient
2010 Mathematics Subject Classification
Primary 14A20. Secondary 14F05, 19L47.