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

## TL;DR

This paper develops the theory of instanton bundles on the flag variety F(0,1,2), providing monadic descriptions, analyzing their moduli space as a GIT quotient, and studying their jumping conics.

## Contribution

It introduces two monadic presentations for instanton bundles on F(0,1,2), characterizes their moduli space as a GIT quotient, and examines the geometry of the stable locus and jumping conics.

## Key findings

- Moduli space of instanton bundles is a geometric GIT quotient.
- Stable instanton bundles form a generically smooth component of dimension 8k-3.
- Analysis of the locus of jumping conics.

## Abstract

Instanton bundles on $\mathbb{P}^3$ 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 $\mathbb{P}^2$. 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 $MI^s_F(k)\subset MI_F(k)$ of stable instanton bundles has a generically smooth component of dim $8k-3$. Finally we study their locus of jumping conics.