New moduli components of rank 2 bundles on projective space

C. Almeida   ; M. Jardim   ; A. S. Tikhomirov   ; S. A. Tikhomirov

Sbornik. Mathematics, Tome 212 (2021) no. 11, pp. 1503-1552

Résumé

We present a new family of monads whose cohomology is a stable rank 2 vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank 2 vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank 2 vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components. Bibliography: 40 titles.

Détail

Keywords: rank 2 bundles, monads, instanton bundles.

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