New moduli components of rank 2 bundles on projective space

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

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Published in:Sbornik. Mathematics 2021-11, Vol.212 (11), p.1503-1552
Main Authors: Almeida, C., Jardim, M., Tikhomirov, A. S., Tikhomirov, S. A.
Format: Article
Language:English
Subjects:
Homology
Infinite series
instanton bundles
monads
rank 2 bundles
Smoothness
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description We present a new family of monads whose cohomology is a stable rank 2 vector bundle on . 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.
doi_str_mv 10.1070/SM9490
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subjects Homology
Infinite series
instanton bundles
monads
rank 2 bundles
Smoothness
title New moduli components of rank 2 bundles on projective space
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