Fourier–Mukai transforms of curves and principal polarizations

Marcello Bernardara

doi:10.1016/j.crma.2007.07.006

Algebraic Geometry

Fourier–Mukai transforms of curves and principal polarizations

Presented by: Michel Raynaud

Marcello Bernardara ¹

¹ Laboratoire J. A. Dieudonné, université de Nice – Sophia Antipolis, parc Valrose, 06108 Nice, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 4, pp. 203-208.

Abstract
Résumé

Given a Fourier–Mukai transform $Φ : D (C) \to D (C^{'})$ between the bounded derived categories of two smooth projective curves, we verify that the induced map $ϕ : J (C) \to J (C^{'})$ between the Jacobian varieties preserves the principal polarization if and only if Φ is an equivalence.

Soit $Φ : D (C) \to D (C^{'})$ une transformation de Fourier–Mukai entre les catégories dérivées bornées de deux courbes lisses projectives. On vérifie que l'application $ϕ : J (C) \to J (C^{'})$ induite entre les variétés jacobiennes préserve les polarisations principales si et seulement si Φ est une équivalence.

Received: 2007-05-09
Accepted: 2007-07-17
Published online: 2007-08-09

DOI: 10.1016/j.crma.2007.07.006

Author's affiliations:

Marcello Bernardara ¹

¹ Laboratoire J. A. Dieudonné, université de Nice – Sophia Antipolis, parc Valrose, 06108 Nice, France

@article{CRMATH_2007__345_4_203_0,
     author = {Marcello Bernardara},
     title = {Fourier{\textendash}Mukai transforms of curves and principal polarizations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {203--208},
     publisher = {Elsevier},
     volume = {345},
     number = {4},
     year = {2007},
     doi = {10.1016/j.crma.2007.07.006},
     language = {en},
}

TY  - JOUR
AU  - Marcello Bernardara
TI  - Fourier–Mukai transforms of curves and principal polarizations
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 203
EP  - 208
VL  - 345
IS  - 4
PB  - Elsevier
DO  - 10.1016/j.crma.2007.07.006
LA  - en
ID  - CRMATH_2007__345_4_203_0
ER  -

%0 Journal Article
%A Marcello Bernardara
%T Fourier–Mukai transforms of curves and principal polarizations
%J Comptes Rendus. Mathématique
%D 2007
%P 203-208
%V 345
%N 4
%I Elsevier
%R 10.1016/j.crma.2007.07.006
%G en
%F CRMATH_2007__345_4_203_0

Marcello Bernardara. Fourier–Mukai transforms of curves and principal polarizations. Comptes Rendus. Mathématique, Volume 345 (2007) no. 4, pp. 203-208. doi : 10.1016/j.crma.2007.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.006/

References
Cited by

[1] C. Birkenhake; H. Lange Complex Abelian Varieties, Grundlehren der Math. Wissenschaften, vol. 302, Springer-Verlag, 1992

[2] P. Griffiths; J. Harris Principles of Algebraic Geometry, Wiley Interscience, 1978

[3] D. Huybrechts Fourier–Mukai Transforms in Algebraic Geometry, Oxford Math. Monographs, Oxford University Press, 2006

Cited by Sources:

Comments - Policy