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Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles

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In this article we study the Gieseker–Maruyama moduli spaces ℬ(e, n) of stable rank 2 algebraic vector bundles with Chern classes c1 = e ∈ {−1, 0} and c2 = n ≥ 1 on the projective space ℙ3. We construct the two new infinite series Σ0 and Σ1 of irreducible components of the spaces ℬ(e, n) for e = 0 and e = −1, respectively. General bundles of these components are obtained as cohomology sheaves of monads whose middle term is a rank 4 symplectic instanton bundle in case e = 0, respectively, twisted symplectic bundle in case e = −1. We show that the series Σ0 contains components for all big enough values of n (more precisely, at least for n ≥ 146). Σ0 yields the next example, after the series of instanton components, of an infinite series of components of ℬ(0, n) satisfying this property.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    A. S. Tikhomirov & D. A. Vassiliev

  2. Yaroslavl State Pedagogical University named after K. D. Ushinskii, Yaroslavl, Russia

    S. A. Tikhomirov

  3. Koryazhma Branch of Northern (Arctic) Federal University named after M. V. Lomonosov, Koryazhma, Russia

    S. A. Tikhomirov

Authors
  1. A. S. Tikhomirov
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  2. S. A. Tikhomirov
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  3. D. A. Vassiliev
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Corresponding authors

Correspondence to A. S. Tikhomirov, S. A. Tikhomirov or D. A. Vassiliev.

Additional information

A. S. Tikhomirov was supported by the Academic Fund Program at the National Research University Higher School of Economics in 2018–2019 (Grant 18–01–0037). D. A. Vassiliev completed the research within the framework of the main research program of the National Research University Higher School of Economics. A. S. Tikhomirov and D. A. Vassiliev were supported by funding within the framework of the State Maintenance Program for the Leading Universities of the Russian Federation 5–100.

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Tikhomirov, A.S., Tikhomirov, S.A. & Vassiliev, D.A. Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles. Sib Math J 60, 343–358 (2019). https://doi.org/10.1134/S0037446619020150

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  • DOI: https://doi.org/10.1134/S0037446619020150

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