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 $c_1(K_X)=0$.
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 $c_1(K_X)=0$.
Abstract: We will discuss Beauville’s paper giving a classification statement for (compact, complex) Kähler manifolds with vanishing first Chern class. The Hilbert scheme of points comes in to construct examples of ``irreducible holomorphic symplectic manifolds’’, one of the pieces appearing in the classification.
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.
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 $n=2$, II.
Abstract: We will finish the discussion of local descriptions of the quotient by a finite group, and use them to give local pictures of $X^{[n]}$, $\operatorname{Sym}^n(X)$, the universal family over $X^{[n]}$, and the maps between them when $X$ is a smooth surface and $n=2$.
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
Abstract: Given a smooth surface $X$, we have the Hilbert scheme of points $X^{[n]}$, the associated Hilbert-Chow morphism to $\operatorname{Sym}^n(X)$, and the universal family over $X^{[n]}$. We will study what these look like when $n=2$.
Time: 2:00-3:30 p.m Place: Jeffery Hall 116
Speaker: Mike Roth (Queen's University)
Title: Examples of subschemes of points II
Abstract: We will use the examples from last time to study some of the global geometry of the Hilbert scheme $X^{[n]}$ when $X$ is a smooth surface, and $n=2$, $3$
Time: 2:00-3:30 p.m Place: Jeffery Hall 116
Speaker: Mike Roth (Queen's University)
Title: Examples of subschemes of points
Abstract: Last time we defined the ‘Hilbert Scheme of points’ of a projective variety $X$. This talk will concentrate on examples of the objects being parameterized. I.e., what is "a subscheme of $X$ with Hilbert polynomial $P(s) = m$?".
Time: 2:00-3:30 p.m Place: Jeffery Hall 116
Speaker: Mike Roth (Queen's University)
Title: Introduction to the Hilbert Scheme of Points II
Abstract: We will finish the introduction to the Hilbert Scheme of points associated to a variety X, and outline some of its applications when X is a smooth surface.
Time: 2:00-3:30 p.m Place: Jeffery Hall 116
Speaker: Mike Roth (Queen's University)
Title: Introduction to the Hilbert Scheme of Points
Abstract: We will introduce the Hilbert Scheme of points associated to a variety X, and outline some of its applications when X is a smooth surface.
Time: 1:30-2:30 p.m Place: Jeffery Hall 422
Speaker: Eric Han (Queen's University)
Title: The Hilbert Scheme of points on a surface and a related combinatorial problem
Abstract: We will introduce the idea of a Hilbert scheme, and in particular the Hilbert scheme of points on a surface. We will also briefly discuss a problem about the ‘limits of multiple points’, which is most properly expressed as the closure of a certain locus in the Hilbert scheme of points.
