Math @ Duke

Publications [#243905] of Ezra Miller
Papers Published
 with Anderson, D; Griffeth, S; Miller, E, Positivity and Kleiman transversality in equivariant Ktheory of homogeneous spaces,
Journal of the European Mathematical Society, vol. 13 no. 1
(2011),
pp. 5784, ISSN 14359855 [math.AG/0808.2785], [DOI:10.4171/JEMS/244], [doi]
(last updated on 2018/01/20)
Abstract: We prove the conjectures of GrahamKumar [GrKu08] and GriffethRam [GrRa04] 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 termthe top onewith a welldefined sign. The vanishing is proved by suitably modifying a geometric argument due to M. Brion in ordinary Ktheory that brings KawamataViehweg vanishing to bear. © European Mathematical Society 2011.


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