A formula with nonnegative terms for the degree of the dual variety of a homogeneous space
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- by Carrado de Concini and Jerzy Weyman PDF
- Proc. Amer. Math. Soc. 125 (1997), 1-8 Request permission
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.References
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Additional Information
- Carrado de Concini
- Affiliation: Department of Mathematics, Scuola Normale Superiore, Pisa, Italy
- MR Author ID: 55410
- Email: deconcin@ux1sns.sns.it
- Jerzy Weyman
- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- MR Author ID: 182230
- ORCID: 0000-0003-1923-0060
- Email: weyman@neu.edu
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1-8
- MSC (1991): Primary 13D25, 14N05; Secondary 13D02, 14M15, 15A72
- DOI: https://doi.org/10.1090/S0002-9939-97-03841-0
- MathSciNet review: 1389514