1. CMB Online first
||Projective plane bundles over an elliptic curve|
We calculate the dimension of cohomology groups for
the holomorphic tangent bundles of each isomorphism
class of the projective plane bundle over an elliptic curve.
As an application, we construct the families
of projective plane bundles, and prove that the families
are effectively parametrized and complete.
Keywords:projective plane bundle, vector bundle, elliptic curve, deformation, Kodaira-Spencer map
Categories:14J10, 14J30, 14D15
2. CMB 2007 (vol 50 pp. 567)
||Exotic Torsion, Frobenius Splitting and the Slope Spectral Sequence |
In this paper we show that any Frobenius split, smooth, projective
threefold over a perfect field of characteristic $p>0$ is
Hodge--Witt. This is proved by generalizing to the case of
threefolds a well-known criterion due to N.~Nygaard for surfaces to be Hodge-Witt.
We also show that the second crystalline
cohomology of any smooth, projective Frobenius split variety does
not have any exotic torsion. In the last two sections we include
Keywords:threefolds, Frobenius splitting, Hodge--Witt, crystalline cohomology, slope spectral sequence, exotic torsion