The Prym variety for a cyclic unramified cover of a hyperelliptic Riemann surface.
The Prym vector bundle and Gunning vector bundle over the Teichmüller space.
The rank of hyperelliptic Jacobians in families of quadratic twists
The variation of the rank of elliptic curves over in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over admits infinitely many quadratic twists of rank . Most elliptic curves have even infinitely many twists of rank and examples of elliptic curves with infinitely many twists of rank are known. There are also certain density results. This paper studies the variation of the...
The rank of the multiplication map for sections of bundles on curves
Sia una curva liscia di genere ed , fasci coerenti su . Sia l'applicazione di moltiplicazione. Qui si dimostra che ha rango massimo se e è un fibrato stabile generico su . Diamo un'interpretazione geometrica dell'eventuale non-surgettività di quando sono fibrati in rette generati da sezioni globali e . Studiamo anche il caso .
The rank-one limit of the Fourier-Mukai transform.
The rationality of some moduli spaces of plane curves
The real genus of the alternating groups.
The reduction of a double covering of a Mumford curve.
The Riemann surface of a uniform dessin.
The Riemann-Roch Theorem and the Independence of the Conditions of Adjointness in the case of a curve for which the tangents at the multiple points are distinct from one another.
The Riemann-Roch theorem on algebraic curves
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.