Ampleness equivalence and dominance for vector bundles
| Autor: | Werner Nahm, F. Laytimi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Semigroup
Hyperbolic geometry 010102 general mathematics Vector bundle Algebraic geometry 01 natural sciences Manifold Combinatorics Mathematics - Algebraic Geometry Computer Science::Emerging Technologies Mathematics::Algebraic Geometry Line bundle Differential geometry 0103 physical sciences FOS: Mathematics Generalized flag variety 010307 mathematical physics Geometry and Topology 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Geometriae Dedicata. 200:77-84 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-018-0360-3 |
| Popis: | Hartshorne in “Ample vector bundles” proved that E is ample if and only if $${\mathcal O}_{P(E)}(1)$$ is ample. Here we generalize this result to flag manifolds associated to a vector bundle E on a complex projective manifold X: For a partition a we show that the line bundle $$ Q_a^s$$ on the corresponding flag manifold $$\mathcal {F}l_s(E)$$ is ample if and only if $$ {\mathcal S}_aE $$ is ample. In particular $$\det Q$$ on $$ {G}_r(E)$$ is ample if and only if $$\wedge ^rE$$ is ample. We give also a proof of the Ampleness Dominance theorem that does not depend on the saturation property of the Littlewood–Richardson semigroup. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink