Displaying 21 – 40 of 41

Showing per page

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

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

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.

Holonomie sans structure de Frobenius et critères d’holonomie

Daniel Caro (2011)

Annales de l’institut Fourier

Ce travail s’inscrit dans le cadre de la théorie des 𝒟 -modules arithmétiques de Berthelot. Nous définissons la notion de 𝒟 -modules arithmétiques holonomes. Lorsque les modules sont munis d’une structure de Frobenius, nous retrouvons la définition d’holonomie de Berthelot. Nous vérifions que l’inégalité de Bernstein et le critère homologique d’holonomie de Virrion restent valables sans l’hypothèse d’une structure de Frobenius. Nous établissons qu’un 𝒟 -module surcohérent (sans structure de Frobenius)...

Homological projective duality

Alexander Kuznetsov (2007)

Publications Mathématiques de l'IHÉS

We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are...

Homology classes of real algebraic sets

Wojciech Kucharz (2008)

Annales de l’institut Fourier

There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets. In particular, such classes are studied on algebraic models of smooth manifolds.

Homology for irregular connections

Spencer Bloch, Hélène Esnault (2004)

Journal de Théorie des Nombres de Bordeaux

Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.

Currently displaying 21 – 40 of 41