Proof of the new gap principle 2

Abstract: In this talk, we will prove Proposition 7.1 of [DGH], the so called "New Gap Principle". We will first prove a couple of lemmas (Lemma 6.3 and Lemma 6.4 of [DGH]) using techniques from enumerative geometry which bounds the number of points on a given curve lying in proper subsets of a certain product of varieties . We then use height bounds of points on non degenerate varieties (Theorem 1.6 and Theorem 6.2 of [DGH]) along with lemmas proven to use an inductive argument to prove the New Gap Principle.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.