On the Construction of Galois Extensions of Function Fields and Number Fields.
On the continued fractions of quadratic surds
On the Converse of Abel's Theorem in Characteristic p.
On the curves through an general point of a smooth surface in IP3.
On the deformation of Artin-Schreier to Kummer
On the determinant of periods with finite monodromy.
On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.
On the Difference of 4-Gonal Linear Systems on some Curves
Let C = (C, g^1/4 ) be a tetragonal curve. We consider the scrollar invariants e1 , e2 , e3 of g^1/4 . We prove that if W^1/4 (C) is a non-singular variety, then every g^1/4 ∈ W^1/4 (C) has the same scrollar invariants.
On the Diophantine equation f(y) - x = 0
On the distribution of ramification points in trigonal curves.
On the distribution of the Fₚ-points on an affine curve in r dimensions
On the enumerative geometry of real algebraic curves having many real branches.
On the Euler number of an orbifold.
On the Exceptional Tangents to a Smooth, Plane Curve.
On the existence of certain families of curves.
On the existence of components of the Hilbert scheme with the expected number of moduli.
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