A formula with nonnegative terms for the degree of the dual variety of a homogeneous space期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A formula with nonnegative terms for the degree of the dual variety of a homogeneous space

Authors:	Carrado de Concini Jerzy Weyman

Institution:	Department of Mathematics, Scuola Normale Superiore, Pisa, Italy ; Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Abstract:	Let be a reductive group and a parabolic subgroup. For every -regular dominant weight $\lambda$ let $X(\lambda )$ denote the variety embedded in the projective space by the embedding corresponding to the ample line bundle $\mathcal L(\lambda )$ . Writing $\lambda =\rho _P+\sum _{i=1}^n m'_i\omega _i$ , we prove that the degree $d(\lambda )^\vee$ of the dual variety to $X(\lambda )$ is a polynomial with nonnegative coefficients in $m'_1,\dots , m'_n$ . In the case of homogeneous spaces we find an expression for the constant term of this polynomial.

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