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Moduli of vector bundles on curves with parabolic structures
Let H be the upper half plane and T a discrete subgroup of AutH. Suppose that H mod Y is of finite measure. This work stems from the question whether there is an algebraic interpretation for the
Semistable sheaves on projective varieties and their restriction to curves
Let X be a nonsingular projective variety of dimension n over an algebraically closed field k. Let H be a very ample line bundle on X. If V is a torsion free coherent sheaf on X we define deg V to be
Frobenius splitting and cohomology vanishing for Schubert varieties
Let k be an algebraically closed field of characteristic p > 0 and X be a projective variety over k. We then have the absolute Frobenius F: X -> X and an injection Ox -* F *6x given by f fP, f e O9x.
Restriction of stable sheaves and representations of the fundamental group
Let X be a projective smooth variety of dimension n over an algebraically closed field k. Let H be an ample line bundle on X. A torsion free sheaf V on X is said to be stable (respectively,
A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices
We exhibit a nice Frobenius splitting σ on G× b where b is the Lie algebra of the Borel group B of upper triangular matrices in the general linear group G = Gln. What is nice about it, is that it
Varieties in positive characteristic with trivial tangent bundle
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Simply connected projective manifolds in characteristic p>0 have no nontrivial stratified bundles
We show that simply connected projective manifolds in characteristic p>0 have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker (Ann. Sc. Norm. Super.
On a Grauert-Riemenschneider vanishing theorem for Frobenius split varieties in characteristicp
This paper is about sheaf cohomology for varieties (schemes) in characteristic $p>0$. We assume the presence of a Frobenius splitting. (See V.B. Mehta and A. Ramanathan, Frobenius splitting and