Wednesday, October 16th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Classical results on canonical embeddings II.

Abstract: We will discuss the Hilbert polynomial and Hilbert function of canonically embedded curves, classical theorems of Noether, Castelnuovo, Enriques-Babbage, and Petri, and work out the minimal free resolutions of the homogenous coordinate rings of canonically embedded curves in small genus.

Wednesday, October 2nd, 2019

Time: 4:30-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Canonically embedded curves II.

Abstract: We will show that the canonical map is always an embedding for non-hyperelliptic curves, understand the canonical map in the hyperelliptic case, and discuss the ‘geometric interpretation’ of the Riemann-Roch theorem, via the canonical embedding.

Note that the seminar is starting later than its usual time, and will only go for an hour this week.

Tuesday, November 27th, 2018

Time: 2:00-3:30 p.m Place: Jeffery Hall 116

Speaker: Mike Roth (Queen's University)

Title: Beauville’s results on classification of Kähler manifolds with $c_1(K_X)=0$, II.

Abstract: We will continue the discussion of Beauville’s paper, focussing on the structure theorem for simply connected Kähler manifolds with $c_1(K_X)=0$.

Tuesday, November 13th, 2018

Time: 2:00-3:30 p.m Place: Jeffery Hall 116

Speaker: Mike Roth (Queen's University)

Title: Local description of the Hilbert scheme when $n=2$, III.

Abstract: We will study $\operatorname{Sym}^n(X)$ and $X^{[n]}$ when $X$ is a smooth surface and $n=2$. We will also deduce some results in the general case.