Complete intersections in spherical varieties

作者：Kaveh Kiumars^*; Khovanskii A G

来源：Selecta Mathematica, New Series, 2016, 22(4): 2099-2141.

DOI：10.1007/s00029-016-0271-9

• Arithmetic and geometric genus
• Complete intersection
• Spherical variety
• Moment polytope
• Newton-Okounkov polytope
• Virtual polytope

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 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 quasi-projective varieties (i.e., not necessarily spherical homogeneous spaces). When the spherical homogeneous space under consideration is a complex torus , our results specialize to well-known results from the Newton polyhedra theory and toric varieties.

• 出版日期2016-10