On Abelian Varieties with Many Endomorphisms and a Conjecture of Shimura's.
On Castelnuovo's equivalence defect.
On Deformations and the Local Torelli Problem of Cyclic Branched Coverings.
On Dimension Theorems of the Varieties of Special Divisors on a Curve.
On J1 (p) and the kernel of the Eisenstein ideal.
On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics
On Picard bundles over Prym varieties.
On rank semistable vector bundles over an irreducible nodal curve of genus
Sia una curva irriducibile nodale di genere aritmetico . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango , su .
On ranks of Jacobian varieties in prime degree extensions
T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials...
On Subvarieties of Abelian Varieties.
On supersingular curves and Abelian varieties.
On the analogue of the division polynomials for hyperelliptic curves.
On the arithmetic of J0 (N) new.
On the class of Brill-Noether loci for Prym varieties.
On the conjectures of Mordell and Lang in positive characteristics.
On the continued fractions of quadratic surds
On the geometry of moduli of curves and line bundles
Here we focus on the geometry of , the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into and we give generators and relations of the rational Picard group of , extending previous work by A. Kouvidakis.
On the height constant for curves of genus two
On the Hodge cycles of Prym varieties
We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.
On the Jacobian conjecture and the configurations of roots.