Yogish I. Holla

Harder-Narasimhan reduction of a principal bundle

Let E be a principal G-bundle over a smooth projective curve over an algebraically closed field k, where G is a reductive linear algebraic group over k. We construct a canonical reduction of E. The uniqueness of canonical reduction is proved under the assumption that the characteristic of k is zero. Under a mild assumption on the characteristic, the uniqueness is also proved when the characteristic of k is positive.

A Generalisation of Nagata's Theorem on Ruled Surfaces

We prove a generalisation of a theorem of Nagata on ruled surface to the case of the fiber bundle E/P → X, associated to a principal G-bundle E. Using this we prove boundedness for the isomorphism classes of semi-stable G-bundles in all characteristics.

Comparison of fundamental group schemes of a projective variety and an ample hypersurface

Let

Poincaré polynomial of the moduli spaces of parabolic bundles

X

TOPOLOGY OF QUADRIC BUNDLES

be a smooth projective variety defined over an algebraically closed field, and let

Extension of structure groups of principal bundles in positive characteristic

L

Brauer group of moduli of principal bundles over a curve

be an ample line bundle over

The Brauer group of desingularization of moduli spaces of vector bundles over a curve

X

On a characterization of finite vector bundles as vector bundles admitting a flat connection with finite monodromy group

. We prove that for any smooth hypersurface

SEMISTABILITY AND NUMERICALLY EFFECTIVENESS IN POSITIVE CHARACTERISTIC

D