On two-dimensional regular local rings and a lifting problem
On unions of scrolls along linear spaces
On unique and almost unique factorization of complete ideals II.
On Unirationality of Supersingular Surfaces.
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
On universal elliptic curves over Igusa curves.
On unlikely intersections of complex varieties with tori
On valuation spectra
On valued function fields II. Regular functions and elements with the uniqueness property.
On valued function fields III. Reductions of algebraic curves.
On Values of Zeta Functions and ?-adic Euler Characteristc.
On vanishing inflection points of plane curves
We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs which take into account the inflection points of the fibres of . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.
On variation of Hodge-Tate structures.
On Varieties Whose Degree is Small with Respect to Codimension.
On vector bundles whose general sections have all projectively equivalent zero-loci
On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors
We extend results on generic strange duality for surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized .
On Witt rings of function fields of real analytic surfaces and curves.
Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points, in the two-dimensional...
On x³ + y³ + z³ = 3μxyz and Jacobi polynomials
On Zariski's theorem in positive characteristic
In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs to the...
On zero-dimensional subschemes of a complete intersections.