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

2017/06/20 by Francesco Malaspina, Malaspina, Francesco, Simone Marchesi +3 · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.06353

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 MI_F(k) of instanton bundles of charge k is a geometric GIT quotient and the open subspace MI^s_F(k)⊂ MI_F(k) of stable instanton bundles has a generically smooth component of dim 8k-3. Finally we study their locus of jumping conics.

Cited by

• ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons

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