Correction to “Cohomology of line bundles on $G/B$”

Lakshmi Bai; C. Musili; C. S. Seshadri

Displaying similar documents to “Correction to “Cohomology of line bundles on $G / B$ ””

A criterion for virtual global generation

Indranil Biswas, A. J. Parameswaran (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Let $X$ be a smooth projective curve defined over an algebraically closed field $k$ , and let $F_{X}$ denote the absolute Frobenius morphism of $X$ when the characteristic of $k$ is positive. A vector bundle over $X$ is called virtually globally generated if its pull back, by some finite morphism to $X$ from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of $k$ is positive, a vector bundle $E$ over $X$ is virtually globally generated if and only...

About $G$ -bundles over elliptic curves

Yves Laszlo (1998)

Annales de l'institut Fourier

Similarity:

Let $G$ be a complex algebraic group, simple and simply connected, $T$ a maximal torus and $W$ the Weyl group. One shows that the coarse moduli space $M_{G} (X)$ parametrizing $S$ -equivalence classes of semistable $G$ -bundles over an elliptic curve $X$ is isomorphic to $[Γ (T) \otimes_{Z} X] / W$ . By a result of Looijenga, this shows that $M_{G} (X)$ is a weighted projective space.

Poincaré bundles for projective surfaces

Nicole Mestrano (1985)

Annales de l'institut Fourier

Similarity:

Let $X$ be a smooth projective surface, $K$ the canonical divisor, $H$ a very ample divisor and $M_{H} (c_{1}, c_{2})$ the moduli space of rank-two vector bundles, $H$ -stable with Chern classes $c_{1}$ and $c_{2}$ . We prove that, if there exists $c_{1}^{'}$ such that $c_{1}$ is numerically equivalent to $2 c_{1}^{'}$ and if $c_{2} - \frac{1}{4} c_{1}^{2}$ is even, greater or equal to $H^{2} + H K + 4$ , then there is no Poincaré bundle on $M_{H} (c_{1}, c_{2}) \times X$ . Conversely, if there exists $c_{1}^{'}$ such that the number $c_{1}^{'} \cdot c_{1}$ is odd or if $\frac{1}{2} c_{1}^{2} - \frac{1}{2} c_{1} \cdot K - c_{2}$ is odd, then there exists a Poincaré bundle on $M_{H} (c_{1}, c_{2}) \times X$ .

Cohomology of line bundles on $G / B$

Lakshmi Bai, C. Musili, C. S. Seshadri (1974)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Line bundles with $c_{1} {(L)}^{2} = 0$ . Higher order obstruction

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We study secondary obstructions to representing a line bundle as the pull-back of a line bundle on $S^{2}$ and we interpret them geometrically.

Displaying similar documents to “Correction to “Cohomology of line bundles on G / B ””

A criterion for virtual global generation

About G -bundles over elliptic curves

Poincaré bundles for projective surfaces

Cohomology of line bundles on G / B

Line bundles with c 1 ⁢ L 2 = 0 . Higher order obstruction

Displaying similar documents to “Correction to “Cohomology of line bundles on $G / B$ ””

About $G$ -bundles over elliptic curves

Cohomology of line bundles on $G / B$

Line bundles with $c_{1} {(L)}^{2} = 0$ . Higher order obstruction