New moduli components of rank 2 bundles on projective space

Author(s)

Almeida, C. ^[1] ; Jardim, M. ^[2] ; Tikhomirov, A. S. ^[3] ; Tikhomirov, S. A. ^[4]

Affiliation

^[1] Univ Fed Minas Gerais, Dept Math, Belo Horizonte, MG - Brazil

^[2] Inst Math Stat & Sci Comp, Dept Math, Campinas - Brazil

^[3] Natl Res Univ Higher Sch Econ, Fac Math, Moscow - Russia

^[4] Yaroslavl State Pedag Univ, Fac Phys & Math, Yaroslavl - Russia

• Document type: Journal article
• Source: SBORNIK MATHEMATICS; v. 212, n. 11, p. 1503-1552, NOV 1 2021.
• Web of Science Citations: 0

Abstract

We present a new family of monads whose cohomology is a stable rank 2 vector bundle on 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. (AU)

• FAPESP's process: 16/14376-0 - Reflexive and torsion free sheaves on projective spaces
• Grantee: Charles Aparecido de Almeida
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• FAPESP's process: 14/08306-4 - Vector bundles over projective spaces
• Grantee: Charles Aparecido de Almeida
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• FAPESP's process: 18/21391-1 - Gauge theory and algebraic geometry
• Grantee: Marcos Benevenuto Jardim
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/03759-6 - Moduli spaces of stable objects on the projective space
• Grantee: Marcos Benevenuto Jardim
• Support Opportunities: Scholarships abroad - Research