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Browsing Pure Mathematics by Subject "algebraic geometry"
Now showing items 1-7 of 7
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Abstract and Explicit Constructions of Jacobian Varieties
(University of Waterloo, 2018-08-10)Abelian varieties, in particular Jacobian varieties, have long attracted interest in mathematics. Their influence pervades arithmetic geometry and number theory, and understanding their construction was a primary motivator ... -
Approximation Constants for Closed Subschemes of Projective Varieties
(University of Waterloo, 2019-06-19)Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the 1840s. The innocent-looking question of how well an arbitrary real algebraic ... -
Divisibility of Discriminants of Homogeneous Polynomials
(University of Waterloo, 2023-08-28)We prove several square-divisibility results about the discriminant of homogeneous polynomials of arbitrary degree and number of variables, when certain coefficients vanish, and give characterizations for when the discriminant ... -
Generalized GCDs as Applications of Vojta’s Conjecture
(University of Waterloo, 2023-08-31)Starting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this ... -
Horospherical geometry: combinatorial algebraic stacks and approximating rational points
(University of Waterloo, 2024-07-17)The purpose of this thesis is to explore and develop several aspects of the theory of horospherical geometry. Horospherical varieties are equipped with the action of a reductive algebraic group such that there is an open ... -
On the Dynamical Wilf-Zeilberger Problem
(University of Waterloo, 2022-08-15)In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by Wilf-Zeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an ... -
The Weil conjectures
(University of Waterloo, 2008-01-24)In discussing the question of rational points on algebraic curves, we are usually concerned with ℚ. André Weil looked instead at curves over finite fields; assembling the counts into a function, he discovered that it ...