Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles

Сибирский математический журнал

D. A. Vassiliev¹  A. S. Tikhomirov²  S. A. Tikhomirov³ 

[1] Koryazhma Branch of Northern (Arctic) Federal University named after M. V. Lomonosov;National Research University Higher School of Economics;Yaroslavl State Pedagogical University named after K. D. Ushinskii

关键词: rank 2 bundles;    moduli of stable bundles;    symplectic bundles;   

DOI  :  10.1134/S0037446619020150

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY