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(t, ℓ)-STABILITY AND COHERENT SYSTEMS

Part of: Surfaces and higher-dimensional varieties Curves

Published online by Cambridge University Press:  09 October 2019

L. BRAMBILA-PAZ  and
O. MATA-GUTIÉRREZ
L. BRAMBILA-PAZ
Affiliation:
CIMAT, Mineral de Valenciana S/N, Apdo. Postal 402, C.P. 36240. Guanajuato, Gto, Mexico e-mail: lebp@cimat.mx
O. MATA-GUTIÉRREZ
Affiliation:
Departamento de Matemáticas, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, C.P. 44430, Guadalajara, Jalisco, Mexico e-mails: osbaldo.mata@academico.udg.mx, osbaldo@cimat.mx
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Abstract

Let X be a non-singular irreducible complex projective curve of genus g ≥ 2. The concept of stability of coherent systems over X depends on a positive real parameter α, given then a (finite) family of moduli spaces of coherent systems. We use (t, ℓ)-stability to prove the existence of coherent systems over X that are α-stable for all allowed α > 0.

MSC classification

Primary: 14H60: Vector bundles on curves and their moduli
Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 661 - 672
Copyright
© Glasgow Mathematical Journal Trust 2019

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