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Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space

University of Pittsburgh, USA, Askold G. Khovanskii, University of Toronto, Canada
2020 Symmetry, Integrability and Geometry: Methods and Applications  
We prove a version of the BKK theorem for the ring of conditions of a spherical homogeneous space G/H. We also introduce the notion of ring of complete intersections, firstly for a spherical homogeneous space and secondly for an arbitrary variety. Similarly to the ring of conditions of the torus, the ring of complete intersections of G/H admits a description in terms of volumes of polytopes.
doi:10.3842/sigma.2020.016 fatcat:mjx2zlkwafc37lfk433dwhxphe