The asymptotic behaviour of symbolic generic initial systems of generic points

Generic initial ideals of points and curves

Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo-Mumford regularity 1+ ab(a− 1)(b− 1)/2 with the exception of the case a = b = 2, where the regularity is 4. Note that ab(a− 1)(b...

An Asymptotic Vanishing Theorem for Generic Unions Of Multiple Points

An asymptotic vanishing theorem for generic unions of multiple points

Theorem. 1.1 Let X be a projective geometrically reduced and irreducible scheme over a field k of (arbitrary) characteristic p and let M , L be line bundles on X with L ample. If p is positive then suppose further that X is smooth in codimension one. For fixed m ≥ 0 there exists d0 = d0(m), depending also on X,L,M, such that for any d ≥ d0 and any generic union Z of (fat) points of multiplicity...

Thematization Strategies in the Generic Moves of Research Article Introductions

Despite the heterogeneity of ideas regarding the definitions of genre, there are also common instances shared among scholars interested in particular aspects of the notion. Swales (1990) and Bhatia (1993) are primarily interested in the sociological and psychological aspects of genre's functioning and construction, respectively.. Swales analyzes the genre of 'article introduction', into four ge...

Integral Points on Generic Fibers

Let P (x, y) be a rational polynomial. If the curve (P (x, y) = k), k ∈ Q, is irreducible and admits an infinite number of points whose coordinates are integers, Siegel’s theorem implies that the curve is rational. We deal with the case where k is a generic value and prove, in the spirit of the Abhyankar-MohSuzuki theorem, that there exists an algebraic automorphism sending P (x, y) to the poly...