The distribution of bidegrees of smooth surfaces in Gr (1, P3).
The divisor of curves with a vanishing theta-null
The divisor of the resultant.
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 dual of the invariant quintic.
The duality of cusp singularities.
The duals of generic hypersurfaces.
The effect of rational maps on polynomial maps
We describe the polynomials P ∈ ℂ[x,y] such that . As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.
The effect on associated prime ideals produced by an extension of the base field.
The Ehrhart polynomial of a lattice -simplex.
The Eisenstein descent on J0 (N).
The embedding dimension of the formal Moduli space of certain curve singularities.
The end curve theorem for normal complex surface singularities
We prove the “End Curve Theorem,” which states that a normal surface singularity with rational homology sphere link is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function whose zero set intersects in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” is described by giving an explicit set of equations describing...
The enumeration of simultaneous higher-order contacts between plane curves
The enumerative geometry of plane cubics. II. Nodal and cuspidal cubics.
The equation x+y = α in multiplicatively dependent unknowns
The equation xyz = x + y + z = 1 in integers of a cubic field.
The Equations Defining Abelian Varieties and Modular Functions.
The Equations for Modular Function Fields of Principal congruence subgroups of prime level.
The equations of conjugacy classes of nilpotent matrices.