Séries d'Eisenstein et fonctions L de courbes elliptiques à multiplication complexe.
In this article we study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and...
A notion of positivity, called Seshadri ampleness, is introduced for a smooth curve in a polarized smooth projective -fold , whose motivation stems from some recent results concerning the gonality of space curves and the behaviour of stable bundles on under restriction to . This condition is stronger than the normality of the normal bundle and more general than being defined by a regular section of an ample rank- vector bundle. We then explore some of the properties of Seshadri-ample curves....
Let Y be a submanifold of dimension y of a polarized complex manifold (X, A) of dimension k ≥ 2, with 1 ≤ y ≤ k−1. We define and study two positivity conditions on Y in (X, A), called Seshadri A-bigness and (a stronger one) Seshadri A-ampleness. In this way we get a natural generalization of the theory initiated by Paoletti in [Paoletti R., Seshadri positive curves in a smooth projective 3-fold, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 1996, 6(4), 259–274] (which...
It is known that for determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not determining. In this paper we give examples of sets which are not determining, but have the Bernstein and generalized Markov properties.
Let be a foliation on a complex, smooth and irreducible projective surface , assume admits a holomorphic first integral . If for some we prove the inequality: . If is rational we prove that the direct image sheaves of the co-normal sheaf of under are locally free; and give some information on the nature of their decomposition as direct sum of invertible sheaves.
We study the local factor at of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.