N. N. Osipov, S. A. Tikhomirov, “On the number of Vedernikov–Ein irreducible components of the moduli space of stable rank 2 bundles on the projective space”, Sibirsk. Mat. Zh., 2018, Volume 59, Number 1,Pages <nobr>136

This article is cited in 6 papers

On the number of Vedernikov–Ein irreducible components of the moduli space of stable rank 2 bundles on the projective space

N. N. Osipov^a, S. A. Tikhomirov^bc

^a Siberian Federal University, Krasnoyarsk, Russia
^b Yaroslavl' State Pedagogical University, Yaroslavl', Russia
^c Koryazhma Branch of Northern (Arctic) Federal University, Koryazhma, Russia

Abstract: We propose a method for finding the exact number of Vedernikov–Ein irreducible components of the first and second types in the moduli space $M(0,n)$ of stable rank 2 bundles on the projective space $\mathbb P^3$ with Chern classes $c_1=0$ and $c_2=n\geq1$. We give formulas for the number of Vedernikov–Ein components and find a criterion for their existence for arbitrary $n\geq1$.

Keywords: stable bundle, Chern classes, moduli space, Pell equations.

UDC: 512.7

Received: 03.02.2017

DOI: 10.17377/smzh.2018.59.112