Speaker: Jerome William Hoffman 教授

Inviter: 贾晓红研究员

Title: Tubular Surfaces and Families of Conics

Language: English

Time & Venue: 2025.06.04 09:00-10:00 南楼N219

Abstract: We start by recalling the definition of rational and unirational varieties. We discuss the famous problem of giving examples of unirational but not rational varieties. This is specialized to conics and quadrics, especially to parametric families of conics. An example of a parametric family of conics is a tubular surface. Next, we recall the theory of syzygies and especially μ-bases. Under a wide set of circumstances, tubular surfaces are rational. From a computational viewpoint, the problem is then to compute rational parameters on a tubular surface. We compare two methods: One, the method of projection, and the other based on syzygies - moving lines.