On the differentiable structure of certain algebraic surfaces

A. Van de Ven

Displaying similar documents to “On the differentiable structure of certain algebraic surfaces”

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

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In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

Vector bundles over real algebraic surfaces and threefolds

Wojciech Kucharz (1986)

Compositio Mathematica

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Orbifold Riemann surfaces and the Yang-Mills-Higgs equations

Ben Nasatyr, Brian Steer (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Fano bundles of rank 2 on surfaces

Michał Szurek, Jarosław A. Wisniewski (1990)

Compositio Mathematica

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Examples of non-ample normal bundles

Norman Goldstein (1984)

Compositio Mathematica

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The Canonical Class and the $C^{\infty}$ Properties of Kähler Surfaces.

Brussee, Rogier (1996)

The New York Journal of Mathematics [electronic only]

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Poincaré bundles for projective surfaces

Nicole Mestrano (1985)

Annales de l'institut Fourier

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

Displaying similar documents to “On the differentiable structure of certain algebraic surfaces”

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vector bundles over real algebraic surfaces and threefolds

Orbifold Riemann surfaces and the Yang-Mills-Higgs equations

Fano bundles of rank 2 on surfaces

Examples of non-ample normal bundles

The Canonical Class and the C ∞ Properties of Kähler Surfaces.

Poincaré bundles for projective surfaces

The Canonical Class and the $C^{\infty}$ Properties of Kähler Surfaces.