The scheme of morphisms from an elliptic curve to a Grassmannian
The Schottky-Jung theorem for Mumford curves
The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.
The Semigroup of a Singular Point of a Curve with Two Equisingular Branches.
The semigroup of values of acurve singularity with several branches.
The Singular Points on the Moduli Spaces for Smooth Curves.
The size of Selmer groups for the congruent number problem.
The small Schottky-Jung locus in positive characteristics different from two
We prove that the locus of Jacobians is an irreducible component of the small Schottky locus in any characteristic different from . The proof follows an idea of B. van Geemen in characteristic and relies on a detailed analysis at the boundary of the - expansion of the Schottky-Jung relations. We obtain algebraically such relations using Mumford’s theory of -adic theta functions. We show how the uniformization theory of semiabelian schemes, as developed by D. Mumford, C.-L. Chai and G. Faltings,...
The Spectrum of Fermat Curves.
The Strong Lefschetz Principle in Algebraic Geometry.
The structure of a local embedding and Chern classes of weighted blow-ups
For a proper local embedding between two Deligne-Mumford stacks and , we find, under certain mild conditions, a new (possibly non-separated) Deligne-Mumford stack , with an etale, surjective and universally closed map to the target , and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to . Moreover, a natural set of weights on the substacks of allows the construction of a universally closed...
The subbundles of decomposable vector bundles over on elliptic curve.
Let C be an elliptic curve and E, F polystable vector bundles on C such that no two among the indecomposable factors of E + F are isomorphic. Here we give a complete classification of such pairs (E,F) such that E is a subbundle of F.
The Tangent Surface of a rational Algebraic Space Curve.
The tautological ring of
We describe the tautological ring of the moduli space of stable -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.
The Torelli map at the boundary of the Schottky space.
The torsion subgroup of a family of elliptic curves over the maximal abelian extension of
We determine explicitly the structure of the torsion group over the maximal abelian extension of and over the maximal -cyclotomic extensions of for the family of rational elliptic curves given by , where is an integer.
The trisecant conjecture.
The underlying real algebraic structure of complex elliptic curves.
The Uniform Position Principle for Curves in Characteristic p.
The universal periods of curves and the Schottky problem
The Weil pairing and the Hilbert symbol.