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.
Time: 2:00-3:30 p.m (Note the special time) Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: The fundamental group of the complement of a nodal plane curve
Abstract: We will finish the proof that the fundamental group of the complement of a plane nodal curve is abelian.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak’s theorems on tangencies IV
Abstract: We will finish the proof of Hartshorne’s conjecture on linear normality, and introduce the problem of computing the fundamental group of the complement of a nodal curve in the plane.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak's theorems on tangencies III
Abstract: We will prove Hartshorne’s conjecture on linear normality of subvarieties of small dimension, in the form of the restatement in terms of secant varieties.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak’s theorems on tangencies II
Abstract: We will prove a result due to F. Zak on the secant variety to a smooth variety (under a certain codimension condition). This result proves a conjecture of Hartshorne on linear normality of subvarieties of small codimension.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Daniel Erman (Wisconsin-Madison)
Title: Big polynomial rings and Stillman’s conjecture
Abstract: Ananyan–Hochster's recent proof of Stillman's conjecture is based on a key principle: if f_1,.., f_r are sufficiently general forms in a polynomial ring, then as the number of variables tends to infinity, they will behave increasingly like independent variables. We show that this principle becomes a theorem if ones passes to a limit of polynomial rings, using either the inverse limit or the ultraproduct. This yields the surprising fact that these limiting rings are themselves polynomial rings (in uncountably many variables). It also yields two new proofs of Stillman's conjecture. This is joint work with Steven Sam and Andrew Snowden.
