Unipotent variations of mixed Hodge structure.
Unique decomposition for a polynomial of low rank
Let F be a homogeneous polynomial of degree d in m + 1 variables defined over an algebraically closed field of characteristic 0 and suppose that F belongs to the sth secant variety of the d-uple Veronese embedding of into but that its minimal decomposition as a sum of dth powers of linear forms requires more than s summands. We show that if s ≤ d then F can be uniquely written as , where are linear forms with t ≤ (d-1)/2, and Q is a binary form such that with ’s linear forms and ’s forms...
Unique range sets and uniqueness polynomials in positive characteristic II
Uniqueness of crepant resolutions and symplectic singularities
We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4- dimensional symplectic singularities is proved. We also give an example of a symplectic singularity which admits two non-equivalent symplectic resolutions.
Uniqueness of equivariant singular Bott-Chern classes
In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion...
Uniqueness of Steiner laws on cubic curves.
Uniqueness properties for spherical varieties
The goal of these lectures is to explain speaker’s results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial invariants for spherical varieties from this class. The problem is to determine whether this set of invariants specifies a spherical variety in this class uniquely (up to an isomorphism). We are interested in three classes: smooth affine varieties, general affine varieties,...
Unirational quartic hypersurfaces
Dopo aver ricordato i principali risultati concernenti l'unirazionalità dell'ipersuperficie quartica generale di (definita su un corpo K qualsiasi) si illustra la costruzione geometrica che permette di provare l'esistenza di una superficie razionale in ogni di , con , e di trovare altri esempi di ipersuperficie quartiche lisce che sono unirazionali oltre a quello dato da B. Segre nel 1960. Si mostra poi come l'analisi delle superficie quartiche monoidali (cioè contenenti un punto triplo...
Unirationality of Enriques surfaces in characteristic two
Unirationality of the moduli spaces of curves of genus 11, 13 (and 12).
Unisecant curves on a general ruled surface.
Unitary K-Homology, SL2 and the Class Group.
Unités elliptiques et groupes de classes
Nous étudions les extensions abéliennes d’un corps quadratique imaginaire et discutons les analogues des théorèmes de Mazur et Wiles.
Unités relatives
Units from 3- and 4-torsion on jacobians of curves of genus 2
Units in the Modular Function Field. I.
Units in the Modular Function Field. II. A full Set of Units.
Units in the Modular Function Field. III. Distribution Relations.
Units in the Modular Function Field. IV. The Siegel Functions are Generators.
Units in the Modular Function Field. V. Iwasawa Theory in the Modular Tower.