Spazi di moduli di fasci aritmeticamente Cohen-Macaulay su varietà di Fano della serie principale

Maria Chiara Brambilla; Daniele Faenzi

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 1, page 71-91
  • ISSN: 0392-4041

Abstract

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In the first part of the paper we complete the classification of the arithmetical Cohen-Macaulay vector bundles of rank 2 on a smooth prime Fano threefold. In the second part, we study some moduli spaces of these vector bundles, using the decomposition of the derived category of X provided by Kuznetsov, when the genus of X is 7 or 9. This allows to prove that such moduli spaces are birational to Brill-Noether varieties of vector bundles on a smooth projective curve Γ . When the second Chern class is low we are able to give a more precise description of the moduli space of rank-2 semistable sheaves with fixed Chern classes 𝐌 X ⁢ ( 2 , c 1 , c 2 ) . If g = 7 , we show that the moduli space 𝐌 X ⁢ ( 2 , 1 , 6 ) is isomorphic to a smooth irreducible Brill-Noether variety of dimension 3. Moreover the set of vector bundles contained in 𝐌 X ⁢ ( 2 , 0 , 4 ) is smooth irreducible of dimension 5. If g = 9 , we prove that 𝐌 X ⁢ ( 2 , 1 , 7 ) is isomorphic to the blow-up of Pic ⁡ ( Γ ) , where Γ is a plane smooth quartic. If g = 12 , an open set of 𝐌 X ⁢ ( 2 , 1 , d ) can be described as a quotient with respect to the action of a semisimple group in terms of monads.

How to cite

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Brambilla, Maria Chiara, and Faenzi, Daniele. "Spazi di moduli di fasci aritmeticamente Cohen-Macaulay su varietà di Fano della serie principale." Bollettino dell'Unione Matematica Italiana 2.1 (2009): 71-91. <http://eudml.org/doc/290586>.

@article{Brambilla2009,
author = {Brambilla, Maria Chiara, Faenzi, Daniele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {2},
number = {1},
pages = {71-91},
publisher = {Unione Matematica Italiana},
title = {Spazi di moduli di fasci aritmeticamente Cohen-Macaulay su varietà di Fano della serie principale},
url = {http://eudml.org/doc/290586},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Brambilla, Maria Chiara
AU - Faenzi, Daniele
TI - Spazi di moduli di fasci aritmeticamente Cohen-Macaulay su varietà di Fano della serie principale
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/2//
PB - Unione Matematica Italiana
VL - 2
IS - 1
SP - 71
EP - 91
LA - ita
UR - http://eudml.org/doc/290586
ER -

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