Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

Kuznetsov, Alexander; Manivel, Laurent; Markushevich, Dimitri

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

Author(s) :

Kuznetsov, Alexander [Auteur]
Steklov Mathematical Institute [Moscow] [SMI | RAS]
Manivel, Laurent [Auteur]
Institut Fourier [IF ]
Markushevich, Dimitri [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Communications in Contemporary Mathematics

Pages :

373-416

Publisher :

World Scientific Publishing

Publication date :

2010-06

ISSN :

0219-1997

HAL domain(s) :

Mathématiques [math]/Géométrie algébrique [math.AG]

English abstract : [en]

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface ...
Show more >It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.Show less >

Language :

Anglais

Popular science :

Non

Comment :

Fano scheme; moduli space; Calabi-Yau variety; projective duality, Hochschild cohomology

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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