Complete intersections in spherical varieties
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Kiumars Kaveh [1] ; A. G. Khovanskii [2]
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[1] University of Pittsburgh
University of Pittsburgh
City of Pittsburgh, Estados Unidos
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[2] University of Toronto
University of Toronto
Canadá
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 2099-2141
- Idioma: inglés
- DOI: 10.1007/s00029-016-0271-9
- Enlaces
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Resumen
Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G/H defined by a generic collection of sections from G-invariant linear systems.Whenever nonempty, all such complete intersections are smooth varieties. We compute their arithmetic genus as well as some of their h p,0 numbers. The answers are given in terms of the moment polytopes and Newton– Okounkov polytopes associated to G-invariant linear systems.We also give a necessary and sufficient condition on a collection of linear systems so that the corresponding generic complete intersection is nonempty. This criterion applies to arbitrary quasiprojective varieties (i.e., not necessarily spherical homogeneous spaces). When the spherical homogeneous space under consideration is a complex torus(C∗)n, our results specialize to well-known results from the Newton polyhedra theory and toric varieties.
