Vol. 308, No. 1, 2020

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

Abdelmoubine Amar Henni

Vol. 308 (2020), No. 1, 41–72

Let 𝕋 be the three-dimensional torus acting on 3 and 3𝕋(c) be the fixed locus of the corresponding action on the moduli space of rank 2 framed instanton sheaves on 3. We prove that 3𝕋(c) consist only of non-locally-free instanton sheaves whose double dual is the trivial bundle 𝒪32. Moreover, we relate these instantons to Pandharipande–Thomas stable pairs and give a classification of their support. This allows us to compute a lower bound on the number of components of 3𝕋(c).

instantons, fixed locus, moduli spaces
Mathematical Subject Classification 2010
Primary: 14F05, 14J10
Received: 17 August 2018
Revised: 10 October 2019
Accepted: 6 June 2020
Published: 3 December 2020
Abdelmoubine Amar Henni
Departamento de Matemática
Universidade Federal de Santa Catarina
Florianópolis, SC