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Integrable Systems and Torelli Theorems for the Moduli Spaces of Parabolic Bundles and Parabolic Higgs Bundles

Published online by Cambridge University Press:  20 November 2018

Indranil Biswas ,
Tomás L. Gómez  and
Marina Logares
Indranil Biswas
Affiliation:
School of Mathematics, Homi Bhabha Road, Bombay 400005, Tata Institute of Fundamental Research, India e-mail: indranil@math.tifr.res.in
Tomás L. Gómez
Affiliation:
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolas Cabrera 15, 28049 Madrid, Spain e-mail: tomas.gomez@icmat.es marina.logares@icmat.es
Marina Logares
Affiliation:
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolas Cabrera 15, 28049 Madrid, Spain e-mail: tomas.gomez@icmat.es marina.logares@icmat.es
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Abstract

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We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weightsystemis generic. When the genus is at least two, using this result we also prove a Torelli theoremfor the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights.The key input in the proofs is a method of J.C. Hurtubise.

Keywords

14D2214D20Keywordsparabolic bundleHiggs fieldTorelli theorem

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 3 , 01 June 2016 , pp. 504 - 520
Copyright
Copyright © Canadian Mathematical Society 2016

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