Publications [#184071] of Ezra Miller

Papers Published

1. with Dave Anderson and Stephen Griffeth, Positivity and Kleiman transversality in equivariant K-theory of homogeneous spaces, Journal of the European Mathematical Society, vol. 13 (2011), pp. 57-84 [math.AG/0808.2785], [DOI:10.4171/JEMS/244]
   (last updated on 2012/12/14)

   Abstract:
   We prove the conjectures of Graham–Kumar and Griffeth­–Ram concerning the alternation of signs in the structure constants for torus-equivariant K-theory of generalized flag varieties G/P. These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a natural group action with finitely many orbits. The computation of the coefficients in the expansion of the equivariant K-class of a subvariety in terms of Schubert classes is reduced to an Euler characteristic using the homological transversality theorem for nontransitive group actions due to S. Sierra. A vanishing theorem, when the subvariety has rational singularities, shows that the Euler characteristic is a sum of at most one term—the top one—with a well-defined sign. The vanishing is proved by suitably modifying a geometric argument due to M. Brion in ordinary K-theory that brings Kawamata­–Viehweg vanishing to bear.