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ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES

Part of: (Co)homology theory Families, fibrations Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  18 December 2014

ABDELMOUBINE AMAR HENNI ,
MARCOS JARDIM  and
RENATO VIDAL MARTINS
ABDELMOUBINE AMAR HENNI
Affiliation:
Universidade Federal de Santa Catarina (UFSC), Departamento de Matemática, Florianópolis-SC, Brazil e-mail: [email protected]
MARCOS JARDIM
Affiliation:
IMECC - UNICAMP, Departamento de Matemática, Caixa Postal 6065, 13083-970 Campinas-SP, Brazil e-mail: [email protected]
RENATO VIDAL MARTINS
Affiliation:
ICEx - UFMG, Departamento de Matemática, Av. Antônio Carlos 6627, 30123-970 Belo Horizonte MG, Brazil e-mail: [email protected]
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Abstract

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We present a construction of framed torsion free instanton sheaves on a projective variety containing a fixed line which further generalises the one on projective spaces. This is done by generalising the so called ADHM variety. We show that the moduli space of such objects is a quasi projective variety, which is fine in the case of projective spaces. We also give an ADHM categorical description of perverse instanton sheaves in the general case, along with a hypercohomological characterisation of these sheaves in the particular case of projective spaces.

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles
Secondary: 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 14F05: Sheaves, derived categories of sheaves and related constructions 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 285 - 321
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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