Bhosle, Usha N. ; Parameswaran, A. J.
(2014)
*Holonomy group scheme of an integral curve*
Mathematische Nachrichten, 287
(17-18).
pp. 1937-1953.
ISSN 0025-584X

Full text not available from this repository.

Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.20...

Related URL: http://dx.doi.org/10.1002/mana.201300117

## Abstract

Let Y be a projective variety over a field k (of arbitrary characteristic). Assume that the normalization X of Y is such that X_{k̅} is normal, math formula being the algebraic closure of k. We define a notion of strong semistability for vector bundles on Y. We show that a vector bundle on Y is strongly semistable if and only if its pull back to X is strongly semistable and hence it is a tensor category. In case dim Y = 1, we show that strongly semistable vector bundles on Y form a neutral Tannakian category. We define the holonomy group scheme G_{Y} of Y to be the Tannakian group scheme for this category. For a strongly semistable principal G-bundle E_{G}, we construct a holonomy group scheme. We show that if Y is an integral complex nodal curve, then the holonomy group of a strongly semistable vector bundle on Y is the Zariski closure of the (topological) fundamental group of Y.

Item Type: | Article |
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ID Code: | 112230 |

Deposited On: | 23 Jan 2018 12:10 |

Last Modified: | 23 Jan 2018 12:10 |

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