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Algebraic Geometry Commons

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Full-Text Articles in Algebraic Geometry

On The Superabundance Of Singular Varieties In Positive Characteristic, Jake Kettinger May 2023

On The Superabundance Of Singular Varieties In Positive Characteristic, Jake Kettinger

Department of Mathematics: Dissertations, Theses, and Student Research

The geproci property is a recent development in the world of geometry. We call a set of points Z\subseq\P_k^3 an (a,b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P to a plane is a complete intersection of curves of degrees a and b. Examples known as grids have been known since 2011. Previously, the study of the geproci property has taken place within the characteristic 0 setting; prior to the work in this thesis, a procedure has been known for creating an (a,b)-geproci half-grid for 4\leq a\leq b, but it was not …


Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra Jan 2015

Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra

College of Graduate Studies: Theses & Dissertations

We examine the automorphism group of configurations of rational curves on $K3$ surfaces. We use the properties of finite automorphisms of $\PP^1$ to examine what restrictions a given elliptic fibration imposes on the possible finite order non-symplectic automorphisms of the $K3$ surface. We also examine the fixed loci of these automorphisms, and construct an explicit fibration to demonstrate the process.


Cassini Ovals As Elliptic Curves, Nozomi Arakaki Jan 2012

Cassini Ovals As Elliptic Curves, Nozomi Arakaki

Theses Digitization Project

The purpose of this project is to show that Cassini curves that are not lemniscates, when b does not equal 1, represent elliptic curves. It is also shown that the cross-ratios of these elliptic curves are either real numbers or represented by complex numbers on the unit circle on the conplex plane.


Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah Jan 2007

Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah

Theses Digitization Project

The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.


Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel May 2005

Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.