Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Gary L. Ebert, Dept. of Mathematical Sciences. Includes bibliographical references.

The Hilbert scheme of \(n\) points in the projective plane parameterizes degree \(n\) zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying interpolation, restriction, and stability properties of certain vector bundles on the plane we fully determine these cones for just over three fourths of all values of \(n\). A general Steiner bundle on \(\mathbb{P}^N\) is a vector bundle \(E\) admitting a resolution of the form \(0 \rightarrow \mathcal{O}_{\mathbb{P}^N} (−1)^s {M \atop \rightarrow} \mathcal{O}^{s+r}_{\mathbb{P}^N} \rightarrow E \rightarrow 0\), where the map \(M\) is general. We complete the classification of slopes of semistable Steiner bundles on \(\mathbb{P}^N\) by showing every admissible slope is realized by a bundle which restricts to a balanced bundle on a rational curve. The proof involves a basic question about multiplication of polynomials on \(\mathbb{P}^1\) which is interesting in its own right. / Mathematics

Access to abstract permanently restricted to Ball State community only / Access to thesis permanently restricted to Ball State community only / Department of Counseling Psychology and Guidance Services

This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.

Includes bibliography. / 281 p ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--Dept. of Pure Mathematics, University of Adelaide, 1978

Thesis (M. Ed.(Opvoedkundige sielkunde))-University of Pretoria, 2006. / Includes bibliographical references. Available on the Internet via the World Wide Web.

Thesis (Ph.D.)--University of Wollongong, 2005. / Typescript. Includes bibliographical references.

Thesis (Psy. D.)--Wheaton College, 2006. / Abstract. Includes bibliographical references (leaves 120-135).

Thesis (Psy. D.)--Wheaton College, 2006. / Abstract. Includes bibliographical references (leaves 120-135).

On s'intéresse à une compactification, due à Ekedahl, Lando, Shapiro et Vainshtein, du champ des courbes lisses munies de fonctions méromorphes d'ordres fixés. Celle-ci est obtenue comme une adhérence du champ de départ dans un champ propre. On commence par en donner deux constructions alternatives et on étudie les déformations de ses points. On la relie par la suite à la compactification à la Harris-Mumford par les revêtements admissibles et on donne une interprétation modulaire des points du bord. / We study a compactification, due to Ekedahl, Lando, Shapiro and Vainshtein, of the stack of smooth curves endowed with meromorphic functions having fixed orders. The original compactification is obtained as the closure of the initial stack in a proper substack. We start by giving two alternative constructions of the E.L.S.V compactification and by studying the deformation theory of its points. We finally link it to the Harris-Mumford compactification by admissible covers and give a modular interpretation of boundary points.