Math @ Duke

Publications [#184071] of Ezra N Miller
Papers Published
 with Dave Anderson and Stephen Griffeth, Positivity and Kleiman transversality in equivariant Ktheory of homogeneous spaces,
Journal of the European Mathematical Society, vol. 13
(2011),
pp. 5784 [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 torusequivariant Ktheory 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 Kclass 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 welldefined
sign. The vanishing is proved by suitably modifying a geometric argument due to M. Brion in ordinary Ktheory that brings Kawamata–Viehweg vanishing to bear.


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