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Title: Instanton bundles on the flag variety $F(0,1,2)$
Author: Malaspina, Francesco
Marchesi, Simone
Pons Llopis, Joan
Keywords: Funcions de diverses variables complexes
Espais analítics
Geometria algebraica
Física matemàtica
Functions of several complex variables
Analytic spaces
Algebraic geometry
Mathematical physics
Issue Date: 18-Dec-2020
Publisher: Centro Edizioni Scuola Normale Superiore di Pisa
Abstract: Instanton bundles on $\mathbb{P}^3$ have been at the core of the research in A1gebraic Geometry during the last thirty years. Motivated by the recent extension of their definition to other Fano threefolds of Picard number one, we develop the theory of instanton bundles on the complete flag variety $F:=F(0,1,2)$ of point-lines on $\mathbb{P}^2$. After giving for them two different monadic presentations, we use it to show that the moduli space $M I_F(k)$ of instanton bundles of charge $k$ is a geometric GIT quotient and the open subspace $M I_F^s(k) \subset M I_F(k)$ of stable instanton bundles has a generically smooth component of $\operatorname{dim} 8 k-3$. Finally we study their locus of jumping conics.
Note: Versió postprint del document publicat a:
It is part of: Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, 2020, vol. 20, num. 4, p. 1469-1505
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ISSN: 0391-173X
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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