Math @ Duke

Publications [#184071] of Ezra 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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