Here we give an upper polynomial bound (as function of but independent on ) for the order of a -subgroup of with minimal surface of general type defined over the field with . Then we discuss the non existence of similar bounds for the dimension as -vector space of the structural sheaf of the scheme .
Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height of the specialized elliptic curve with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient over all nontorsion P ∈ E(K).
Let C be a smooth curve of genus g. For each positive integer r the birational r-gonality sr(C) of C is the minimal integer t such that there is L ∈ Pict(C) with h0(C,L) = r + 1. Fix an integer r ≥ 3. In this paper we prove the existence of an integer gr such that for every integer g ≥ gr there is a smooth curve C of genus g with sr+1(C)/(r + 1) > sr(C)/r, i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails
Let (S, H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c 1(E), H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of coherent sheaves of different ranks on S, we prove our main theorem: polarized K3 surface which...
Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.
Dato un insieme di punti nello spazio proiettivo, si costruisce un esplicito ideale canonico nel suo anello di coordinate . Si descrivono le componenti omogenee di e la struttura della mappa di moltiplicazione , dove . Tra le applicazioni ci sono varie caratterizzazioni di insiemi di punti coomologicamente uniformi, disuguaglianze nelle loro funzioni di Hilbert, il calcolo del primo modulo delle sizigie di in casi particolari, una generalizzazione della «trasformata di Gale» a trasformate...