Instanton bundles on P3 have been at the core of the research in Algebraic 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 P2. After giving for them two different monadic presentations, we use it to show that the moduli space MIF (k) of instanton bundles of charge k is a geometric GIT quotient and the open subspace MIs(k) ⇢ MIF (k) of stable instanton bundles has a generically smooth component of dim 8k −3. Finally we study their locus of jumping conics.

Instanton bundles on the flag variety F(0,1,2) / Malaspina, Francesco; Marchesi, Simone; Pons-Llopis, Juan Francisco. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 20:4(2020), pp. 1469-1505. [10.2422/2036-2145.201801_003]

Instanton bundles on the flag variety F(0,1,2)

Malaspina, Francesco;Pons-Llopis, Juan Francisco
2020

Abstract

Instanton bundles on P3 have been at the core of the research in Algebraic 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 P2. After giving for them two different monadic presentations, we use it to show that the moduli space MIF (k) of instanton bundles of charge k is a geometric GIT quotient and the open subspace MIs(k) ⇢ MIF (k) of stable instanton bundles has a generically smooth component of dim 8k −3. Finally we study their locus of jumping conics.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2859410