Bethe ansatz, inverse scattering transform and tropical Riemann theta function in a periodic soliton cellular automaton for .
Betti numbers for the Hilbert function strata of the punctual Hilbert scheme in two variables.
Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
We asymptotically estimate from above the expected Betti numbers of random real hypersurfaces in smooth real projective manifolds. Our upper bounds grow as the square root of the degree of the hypersurfaces as the latter grows to infinity, with a coefficient involving the Kählerian volume of the real locus of the manifold as well as the expected determinant of random real symmetric matrices of given index. In particular, for large dimensions, these coefficients get exponentially small away from...
Betti numbers of real elliptic surfaces. (Nombres de Betti des surfaces elliptiques réelles.)
Beweis einer Vermutung von Hartshorne für den Fall homogener Mannigfaltigkeiten.
Beweis eines Riemannschen Satzes.
Beweis eines Satzes über rationale Curven
Beweis eines Satzes von Bertini über lineare Systeme ganzer Functionen
Beweis eines Satzes von Bertini über lineare Systeme ganzer Functionen. II.
Beweis eines Satzes von Riemann über ...-Charakteristiken.
Beyond two criteria for supersingularity: coefficients of division polynomials
Let be a cubic, monic and separable polynomial over a field of characteristic and let be the elliptic curve given by . In this paper we prove that the coefficient at in the –th division polynomial of equals the coefficient at in . For elliptic curves over a finite field of characteristic , the first coefficient is zero if and only if is supersingular, which by a classical criterion of Deuring (1941) is also equivalent to the vanishing of the second coefficient. So the zero loci...
Bicyclotomic polynomials and impossible intersections
In a recent paper we proved that there are at most finitely many complex numbers such that the points and are both torsion on the Legendre elliptic curve defined by . In a sequel we gave a generalization to any two points with coordinates algebraic over the field and even over . Here we reconsider the special case and with complex numbers and .
Bielliptic Abelian Surfaces.
Biextensions alternées
Bi-extensions associated to divisors on abelian varieties and theta functions
Big groups of automorphisms of some Klein surfaces.
Sea Xp una superficie de Klein compacta con borde de gen algebraico p ≥ 2. Se sabe que si G es un grupo de automorfismos de Xp entonces |G| ≤ 12(p- 1). Se dice que G es un grupo grande de gen p si |G| > 4(p -1). En el presente artículo se halla una familia de enteros p para los que el único grupo grande de gen p son los grupos diédricos. Esto significa que, en términos del gen real introducido por C. L. May, para tales valores de p no existen grupos grandes de gen real p.
Big Schottky.
Biliaisons élémentaires en codimension 2
Un théorème de Strano montre que si une courbe gauche localement Cohen-Macaulay n’est pas minimale dans sa classe de biliaison, elle admet une biliaison élémentaire strictement décroissante. R. Hartshorne a récemment donné une nouvelle preuve de ce résultat en le plaçant dans un contexte plus général. Dans cet article on apporte une précision, en utilisant les techniques introduites par Hartshorne : on montre que si un sous-schéma de codimension localement Cohen-Macaulay de n’est pas minimal...
Bilinear forms and extremal Kähler vector fields associated with Kähler classes.
Bilinear three-cycles on the projective line.