On the existence of curves in with stable normal bundle
We prove that for integers n,d,g such that n ≥ 4, g ≥ 2n and d ≥ 2g + 3n + 1, the general (smooth) curve C in with degree d and genus g has a stable normal bundle .
On the existence of curves with maximal rank in Pn.
On the existence of k-normal curves of given degree and genus in projective spaces.
We find some ranges for the 4-tuples of integers (d,g,n,r) for which there is a smooth connected non-degenerate curve of degree d and genus g, which is k-normal for every k ≤ r.
On the existence of special divisors on singular curves
On the existence of supersingular curves of given genus.
On the existence of Weierstrass points whose first non-gaps are five.
On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.
A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs...
On the field of definition of superspecial polarized abelian varieties and type numbers
On the Gauss maps of space curves in characteristic p
On the Gauss maps of space curves in characteristic p, II
On the general hyperplane section of a projective curve.
On the generalized theta divisor.
On the Geometrie Genera of Projective Curves.
On the geometry of algebraic curves having many real components.
We show that there is a large class of nonspecial effective divisors of relatively small degree on real algebraic curves having many real components i.e. on M-curves. We apply to 1. complete linear systems on M-curves containing divisors with entirely real support, and 2. morphisms of M-curves into P1.
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 Gieseker-Petri Map for Rank 2 vector bundles.
On the gonality of curves in
Here we study the gonality of several projective curves which arise in a natural way (e.gċurves with maximal genus in , curves with given degree and genus for all possible , if and with large for arbitrary ).
On the graded Betti numbers for large finite subsets of curves
We prove a recent conjecture of S. Lvovski concerning the periodicity behaviour of top Betti numbers of general finite subsets with large cardinality of an irreducible curve C ⊂ ℙⁿ.
On the graded Betti numbers of plane algebraic curves.
On the group orders of elliptic curves over finite fields