Intersection homology of toric varieties and a conjecture of Kalai | Zendy

Tom Braden | Zendy; Robert MacPherson | Zendy

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Intersection homology of toric varieties and a conjecture of Kalai

Author(s) -

Tom Braden,

Robert MacPherson

Publication year - 1999

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050098

Subject(s) - mathematics , conjecture , intersection homology , homology (biology) , intersection (aeronautics) , complete intersection , pure mathematics , intersection theory , combinatorics , mathematical analysis , geography , biology , cohomology , genetics , gene , differential algebraic equation , ordinary differential equation , cartography , differential equation

. We prove an inequality, conjectured by Kalai, relating the g-polynomials of a polytope P, a face F, and the quotient polytope P/F, in the case where P is rational. We introduce a new family of polynomials g(P,F), which measures the complexity of the part of P“far away” from the face F; Kalai's conjecture follows from the nonnegativity of these polynomials. This nonnegativity comes from showing that the restriction of the intersection cohomology sheaf on a toric variety to the closure of an orbit is a direct sum of intersection homology sheaves.

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