Alexey A. Kytmanov, Sergey A. Tikhomirov, “On the dimensions of components of stable rank $2$ vector bundles with odd determinant on $\mathbb{P}^{3}$”, J. Sib. Fed. Univ. Math. Phys., 2026, Volume 19, Issue 1,Pages 65

On the dimensions of components of stable rank $2$ vector bundles with odd determinant on $\mathbb{P}^{3}$

Alexey A. Kytmanov^a, Sergey A. Tikhomirov^b

^a Institute for Advanced Technologies and Industrial Programming, MIREA — Russian Technological University, Moscow, Russian Federation
^b Ushinsky Yaroslavl State Pedagogical University, Yaroslavl, Russian Federation

Abstract: We prove that the irreducible components of the infinite series of stable rank $2$ vector bundles on complex three-dimensional projectice space with odd determinant, constructed in 2019 by A. S. Tikhomirov, S. A. Tikhomirov, and D. A. Vasiliev, always have a dimension higher than the dimension predicted by the deformation theory.

Keywords: vector bundles, sheaves, moduli space, dimensions of components.

UDC: 517.9

Received: 10.06.2025
Received in revised form: 05.08.2025
Accepted: 27.09.2025

Language: English