The Complete Classification of Fibres in Pencils of Curves of Genus Two.
The complex geometry of an integrable system
In this paper, a finite dimensional algebraic completely integrable system is considered. We show that the intersection of levels of integrals completes into an abelian surface (a two dimensional complex algebraic torus) of polarization and that the flow of the system can be linearized on it.
The Congruences of Clausen- von Staudt and Kummer for Bernoulli-Hurwitz Numbers.
The curve , is not set-theoretic complete intersection of two quartic surfaces
The cuspidal torsion packet on hyperelliptic Fermat quotients
Let be a prime, be the non-singular projective curve defined over by the affine model , the point of at infinity on this model, the Jacobian of , and the albanese embedding with as base point. Let be an algebraic closure of . Taking care of a case not covered in [12], we show that consists only of the image under of the Weierstrass points of and the points and , where denotes the torsion points of .
The cyclic homology and K-theory of curves.
The degree of rational cuspidal curves.
The degree of the secant variety and the join of monomial curves.
A monomial curve is a curve parametrized by monomials. The degree of the secant variety of a monomial curve is given in terms of the sequence of exponents of the monomials defining the curve. Likewise, the degree of the join of two monomial curves is given in terms of the two sequences of exponents.
The Deuring-Safarevic Formula Revisited.
The dimension of the Chow variety of curves
The dimension of the derived category of elliptic curves and tubular weighted projective lines
We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal.
The Diophantine equation f(x) = g(y)
The Discriminants of a Series of Unimodular Singularities of Space Curves.
The discriminants of curves of genus 2
The divisor of curves with a vanishing theta-null
The Drinfeld Modular Jacobian has connected fibers
We study the integral model of the Drinfeld modular curve for a prime . A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod . A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of which, after contractions in...
The Eisenstein descent on J0 (N).
The embedding dimension of the formal Moduli space of certain curve singularities.
The enumeration of simultaneous higher-order contacts between plane curves
The enumerative geometry of plane cubics. II. Nodal and cuspidal cubics.