In this paper we deal with a particular class of rank two vector bundles (emph{instanton} bundles) on the Fano threefold of index one $F:=mathbb{F}_1 imes mathbb{P}^1$. We show that every instanton bundle on $F$ can be described as the cohomology of a monad whose terms are free sheaves. Furthermore we prove the existence of instanton bundles for any admissible second Chern class and we construct a nice component of the moduli space where they sit. Finally we show that minimal instanton bundles (i.e. with the least possible degree of the second Chern class) are aCM and we describe their moduli space.

Instanton bundles on P1×F1 / Antonelli, Vincenzo; Casnati, Gianfranco; Genc, Ozhan. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 49:8(2021), pp. 3594-3613. [10.1080/00927872.2021.1901291]

Instanton bundles on P1×F1

Vincenzo Antonelli;Gianfranco Casnati;Ozhan Genc
2021

Abstract

In this paper we deal with a particular class of rank two vector bundles (emph{instanton} bundles) on the Fano threefold of index one $F:=mathbb{F}_1 imes mathbb{P}^1$. We show that every instanton bundle on $F$ can be described as the cohomology of a monad whose terms are free sheaves. Furthermore we prove the existence of instanton bundles for any admissible second Chern class and we construct a nice component of the moduli space where they sit. Finally we show that minimal instanton bundles (i.e. with the least possible degree of the second Chern class) are aCM and we describe their moduli space.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2957777