Bounds and definablity over fields.
Bounds for Castelnuovo's regularity and the genus of projective varieties
Bounds for Chern classes of semistable vector bundles on complex projective spaces
This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on and a generalization of the presented method to r-bundles on is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.
Bounds for rational points on twists of constant hyperelliptic curves.
Bounds for stable bundles and degrees of Weierstrass schemes.
Bounds for the anticanonical bundle of a homogeneous projective rational manifold.
Bounds for the degrees in the membership test for a polynomial ideal
Bounds for the minimal solution of genus zero diophantine equations
Bounds for the multiplicity of almost complete intersections.
Bounds for the number of connected components and the first Betti number mod two of a real algebraic surface
Bounds for the number of moduli for irregular varieties of general type.
Bounds for the order of the Tate-Shafarevich group
Bounds on Castelnuovo-Mumford regularity for divisors on rational normal scrolls.
The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls.
Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings.
Bounds on degrees of projective schemes.
Bounds on multisecant lines.
The purpose of this paper is twofold. First, we give an upper bound on the order of a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we give an explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine a standard linking theorem. These results are tied together by the construction of sharp examples for the bound,...
Bounds on polarizations of abelian varieties over finite fields.
Bounds on the denominators in the canonical bundle formula
In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If is the Cartier index of the fibre, it was expected that would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in , we provide a bound and an example where the smallest integer that clears the denominators of the moduli part is . Moreover we prove that even locally the denominators depend...
Bounds on the number of non-rational subfields of a function field.
Bounds on the Serre cohomology of projective varieties