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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)...

Homogeneous polynomials with isomorphic Milnor algebras

Imran Ahmed (2010)

Czechoslovak Mathematical Journal

We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.

Homological Mirror Symmetry for manifolds of general type

Anton Kapustin, Ludmil Katzarkov, Dmitri Orlov, Mirroslav Yotov (2009)

Open Mathematics

In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.

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...

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