On rank 3 instanton bundles on projective 3 space

Abstract: We investigate rank $3$ instanton bundles on $\mathbb{P}^3$ of charge $n$ and its correspondence with rational curves of degree $n+3$. in order to prove that the generic stable rank 3 ’t Hooft bundle of charge n is a smooth point in the moduli space of rank 3 vector bundles of Chern classes (0,n,0). Additionally, for $n=2$ we present a correspondence between stable rank $3$ instanton bundles and stable rank $2$ reflexive linear sheaves and we prove that the moduli space of rank $3$ stable locally free sheaves on $\mathbb{P}^3$ of Chern classes $(0,2,0)$ is irreducible, generically smooth of dimension 16. (Joint work with D. R. Santiago, D. D. Silva, and L. S. Sobral)

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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