On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$

Abstract

Let $\mathbb{T}$ be the three dimensional torus acting on ${\mathbb{P}}^3$ and ${\mathcal{M}}_{{\mathbb{P}}^3}^{\mathbb{T}}(c)$ be the fixed locus of the corresponding action on the moduli space of rank $2$ framed instanton sheaves on ${\mathbb{P}}^3.$ In this work, we prove that ${\mathcal{M}}_{{\mathbb{P}}^3}^{\mathbb{T}}(c)$ consist only of non locally-free instanton sheaves whose double dual is the trivial bundle ${\mathcal{O}}_{{\mathbb{P}}^3}^{\oplus 2}$. Moreover, We relate these instantons to Pandharipande-Thomas stable pairs and give a classification of their support. This allows to compute a lower bound on the number of components of ${\mathcal{M}}_{{\mathbb{P}}^3}^{\mathbb{T}}(c).$

27 pages; corrections in section 4 and non primitive case added for c=3

References in corpus (3)

• Two infinite series of moduli spaces of rank 2 sheaves on ${\mathbb{P}}^3$
• Moduli spaces of rank 2 instanton sheaves on the projective space
• Multiple Structures

Cited by in corpus (1)

• Torsion free instanton sheaves on the blow-up of ${\mathbb{P}}^3$ at a point