Positivity of vector bundles on homogeneous varieties
| Autor: | D. S. Nagaraj, Krishna Hanumanthu, Indranil Biswas |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Abelian variety
Pure mathematics Computer Science::Information Retrieval General Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Vector bundle Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 01 natural sciences 14C20 14K12 Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Homogeneous 0103 physical sciences Seshadri constant FOS: Mathematics Computer Science::General Literature 010307 mathematical physics 0101 mathematics Algebraic Geometry (math.AG) Projective variety Mathematics |
| Zdroj: | International Journal of Mathematics. 31:2050097 |
| ISSN: | 1793-6519 0129-167X |
| DOI: | 10.1142/s0129167x20500974 |
| Popis: | We study the following question: Given a vector bundle on a projective variety $X$ such that the restriction of $E$ to every closed curve $C \,\subset\, X$ is ample, under what conditions $E$ is ample? We first consider the case of an abelian variety $X$. If $E$ is a line bundle on $X$, then we answer the question in the affirmative. When $E$ is of higher rank, we show that the answer is affirmative under some conditions on $E$. We then study the case of $X \,=\, G/P$, where $G$ is a reductive complex affine algebraic group, and $P$ is a parabolic subgroup of $G$. In this case, we show that the answer to our question is affirmative if $E$ is $T$--equivariant, where $T\, \subset\, P$ is a fixed maximal torus. Finally, we compute the Seshadri constant for such vector bundles defined on $G/P$. Final version; 11 pages; to appear in International Journal of Mathematics |
| Databáze: | OpenAIRE |
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