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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Carrado de Concini and Jerzy Weyman
Journal: Proc. Amer. Math. Soc. 125 (1997), 1-8
MSC (1991): Primary 13D25, 14N05; Secondary 13D02, 14M15, 15A72
MathSciNet review: 1389514
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Abstract: Let $G$ be a reductive group and $P$ a parabolic subgroup. For every $P$-regular dominant weight $\lambda $ let $X(\lambda )$ denote the variety $G/P$ 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 $G/B$ we find an expression for the constant term of this polynomial.


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Additional Information

Carrado de Concini
Affiliation: Department of Mathematics, Scuola Normale Superiore, Pisa, Italy
Email: deconcin@ux1sns.sns.it

Jerzy Weyman
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: weyman@neu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03841-0
PII: S 0002-9939(97)03841-0
Received by editor(s): January 27, 1995
Additional Notes: The second author was partially supported by NSF grant #DMS-9104867
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1997 American Mathematical Society