On rank 3 instanton bundles on P3$\mathbb {P}^3$

A. V. Andrade, D. R. Santiago, D. D. Silva and L. C. S. Sobral

Mathematische Nachrichten, 2024, vol. 297, issue 8, 2814-2827

Abstract: We investigate rank 3 instanton vector bundles on P3$\mathbb {P}^3$ of charge n$n$ and its correspondence with rational curves of degree n+3$n+3$. For n=2$n=2$, we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes (c1,c2,c3)=(−1,3,3)$(c_1,c_2,c_3)=(-1,3,3)$ and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above to prove that the moduli space of rank 3 instanton bundles on P3$\mathbb {P}^3$ of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on P3$\mathbb {P}^3$ of Chern classes (c1,c2,c3)=(0,2,0)$(c_1,c_2,c_3)=(0,2,0)$. This moduli space is irreducible, has dimension 16 and its generic point corresponds to a generalized't Hooft instanton bundle.

Date: 2024
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