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

• Published in: Mathematische Nachrichten 2024-08, Vol.297 (8), p.2814-2827
• Main Authors: Andrade, A. V., Santiago, D. R., Silva, D. D., Sobral, L. C. S.
• Format: Article
• Language: English
• Subjects: Hartshorne–Serre correspondence; instanton bundles; Instantons; moduli spaces; Sheaves
• ISSN: 0025-584X; 1522-2616
• DOI: 10.1002/mana.202200332

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.