Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T07:32:22.607Z Has data issue: false hasContentIssue false

PARABOLIC HIGGS BUNDLES AND $\Gamma $-HIGGS BUNDLES

Published online by Cambridge University Press:  19 August 2013

INDRANIL BISWAS
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India email indranil@math.tifr.res.in
SOURADEEP MAJUMDER*
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India email indranil@math.tifr.res.in
MICHAEL LENNOX WONG
Affiliation:
Chair of Geometry, Mathematics Section, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland email michael.wong@epfl.ch
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate parabolic Higgs bundles and $\Gamma $-Higgs bundles on a smooth complex projective variety.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Biswas, I., ‘Parabolic bundles as orbifold bundles’, Duke Math. J. 88 (2) (1997), 305325.CrossRefGoogle Scholar
Borne, N., ‘Fibrés paraboliques et champ des racines’, Int. Math. Res. Not. 2007 (16) (2007), Article ID rnm049, 38 pages.CrossRefGoogle Scholar
Cadman, C., ‘Using stacks to impose tangency conditions on curves’, Amer. J. Math. 129 (2) (2007), 405427.CrossRefGoogle Scholar
Deligne, P., Equations Différentielles à Points Singuliers Réguliers, Lecture Notes in Mathematics, 163 (Springer, Berlin, 1970).CrossRefGoogle Scholar
Esnault, H. and Viehweg, E., Lectures on Vanishing Theorems, DMV Seminar, 20 (Birkhäuser, Basel, 1992).CrossRefGoogle Scholar
Gómez, T. L., ‘Algebraic stacks’, Proc. Indian Acad. Sci. Math. Sci. 111 (1) (2001), 131.CrossRefGoogle Scholar
Hitchin, N. J., ‘The self-duality equations on a Riemann surface’, Proc. Lond. Math. Soc. 55 (1987), 59126.CrossRefGoogle Scholar
Hitchin, N. J., ‘Stable bundles and integrable systems’, Duke Math. J. 54 (1) (1987), 91114.CrossRefGoogle Scholar
Laumon, G. and Moret-Bailly, L., Champs Algébriques (Springer, Berlin, 2000).CrossRefGoogle Scholar
Mac Lane, S., Categories for the Working Mathematician, 2nd edn. Graduate Texts in Mathematics, 5 (Springer, New York, 1998).Google Scholar
Maruyama, M. and Yokogawa, K., ‘Moduli of parabolic stable sheaves’, Math. Ann. 293 (1992), 7799.CrossRefGoogle Scholar
Mehta, V. and Seshadri, C., ‘Moduli of vector bundles on curves with parabolic structures’, Math. Ann. 248 (1980), 205239.CrossRefGoogle Scholar
Namba, M., Branched Coverings and Algebraic Functions, Pitman Research Notes in Mathematics, 161 (Longman Scientific & Technical, Harlow, 1987).Google Scholar
Simpson, C. T., ‘Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization’, J. Amer. Math. Soc. 1 (1988), 867918.CrossRefGoogle Scholar
Vistoli, A., ‘Intersection theory on algebraic stacks and on their moduli spaces’, Invent. Math. 97 (1989), 613670.CrossRefGoogle Scholar
Vistoli, A., Notes on Grothendieck topologies, fibrered categories and descent theory,http://homepage.sns.it/vistoli/descent.pdf, 2008.Google Scholar
Yokogawa, K., ‘Infinitesimal deformations of parabolic Higgs sheaves’, Internat. J. Math. 6 (1995), 125148.CrossRefGoogle Scholar