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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 $M_{H} (c_{1}, c_{2}) \times X$ .

Points at Infinity on the Fermat Curves

D.E. Rohrlich (1977)

Inventiones mathematicae

Polarized surfaces $(X, L)$ with $g (L) = q (X) + m$ and $h^{0} (L) \geq m + 2$

Yoshiaki Fukuma (2003)

Rendiconti del Seminario Matematico della Università di Padova

Polynomial periodicity for Betti numbers of covering surfaces.

Eriko Hironaka (1992)

Inventiones mathematicae

Positive Curves in Polarized Manifolds.

L. Badescu, M.C. Beltrametti (1997)

Manuscripta mathematica

Positivity on subvarieties and vanishing of higher cohomology

Alex Küronya (2013)

Annales de l’institut Fourier

We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.

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Pencils of minimal degree on curves on a K3 surface.

Petri's Approach to the Study of the Ideal Associated to a Special Divisor.

Picard numbers of surfaces in 3-dimensional weighted projective spaces.

Pluriadjoint Bundles of Polarized Surfaces.

Pluricanonical systems on minimal algebraic varieties.

Plurigenera of regular threefolds.

Poincaré bundles for projective surfaces

Points at Infinity on the Fermat Curves

Polarized surfaces $(X, L)$ with $g (L) = q (X) + m$ and $h^{0} (L) \geq m + 2$

Polynomial periodicity for Betti numbers of covering surfaces.

Positive Curves in Polarized Manifolds.

Positivity on subvarieties and vanishing of higher cohomology

Postulation of Canonical Curves in IP3.

Primitive Line Bundles on Abelian Threefolds.

Primitive linear series on curves.

Primitives des fonctions élémentaires

Principal parts of line bundles on toric varieties

Projective manifolds whose tangent bundles are numerically effective.

Projective Models Enriques Surfaces.

Projective Models of Shioda Modular Surfaces.

Currently displaying 1 – 20 of 24