On certain Galois representations related to the modular curve
On certain twisted families of elliptic curves of rank 8.
On Chebyshev polynomials and maximal curves
On Clifford's theorem for rank-3 bundles.
In this paper we obtain bounds on h0(E) where E is a semistable bundle of rank 3 over a smooth irreducible projective curve X of genus g ≥ 2 defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability s1(E), s2(E). We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.
On commutativity and ovals for a pair of symmetries of a Riemann surface
We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry having g+1-q...
On conjugacy of p-gonal automorphisms of Riemann surfaces.
On counterexamples to local-global divisibility in commutative algebraic groups
On cubics and quartics through a canonical curve
We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projective plane, whose Steinerian curve equals the canonical curve
On curves with a theta-characteristic whose space of sections has dimension 4.
On curves with natural cohomology and their deficiency modules
The minimal free resolution of the Hartshorne-Rao module of a curve with natural cohomology is studied, and conditions are given on the degrees and the ranks of the terms of this resolution.
On deformation of maximally degenerate stable marked curves and Oda's problem.
On Deformations and the Local Torelli Problem of Cyclic Branched Coverings.
On deformations of monomial curves
On dihedral algebraic function fields
On Dimension Theorems of the Varieties of Special Divisors on a Curve.
On fixed points of automorphisms of non-orientable unbordered Klein surfaces.
On formal groups obtained from symmetric powers
On galois automorphisms of the fundamental group of the projective line minus three points.
On Galois module structure of the cohomology groups of an algebraic variety.
On Galois representations arising from towers of coverings of P1 ... .