Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Curves Seminar

Curves Seminar - Mike Roth (Queen's University)

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 $c_1(K_X)=0$.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, November 20th, 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 $c_1(K_X)=0$.

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.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, November 6th, 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 $n=2$, 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 $n=2$.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, October 30th, 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

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 $n=2$.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, October 9th, 2018

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 $P(s) = m$?".

Curves Seminar - Eric Han (Queen's University)

Thursday, August 30th, 2018

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.

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