UC Riverside Algebraic Geometry Seminar

UC Riverside Algebraic Geometry Seminar


The UC Riverside Algebraic Geometry Seminar meets on Tuesdays from 11:00am to 12:00pm. We usually meet in Skye 268, but the meetings are online via Zoom during Winter 2021. For more information you may contact Ziv Ran (ziv.ran@ucr.edu), Jose Gonzalez (jose.gonzalez@ucr.edu) or Patricio Gallardo (patricio.gallardocandela@ucr.edu). Please find our schedule below. For information about reimbursements for our visitors click here.



Winter 2021

Date Speaker Title Abstract
Tuesday, January 19, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Luca Schaffler
KTH Royal Institute of Technology
Compactifications of moduli of points and lines in the projective plane. Projective duality identifies the moduli space Bn parametrizing configurations of n general points in the projective plane with X(3,n), parametrizing configurations of n general lines in the dual projective plane. When considering degenerations of such objects, it is interesting to compare different compactifications of the above moduli spaces. In this work, we consider Gerritzen-Piwek's compactification of Bn and Kapranov's Chow quotient compactification of X(3,n), and we show that they have isomorphic normalizations. We also construct an alternative compactification parametrizing all possible n-pointed central fibers of Mustafin joins associated to one-parameter degenerations of n points in the projective plane, which was proposed by Gerritzen and Piwek. We fully describe this alternative compactification for n=5,6. This is joint work with Jenia Tevelev.
Tuesday, January 26, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Changho Han
University of Georgia
TBA TBA
Tuesday, February 2, 2021
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Dustin Ross
San Francisco State University
Putting the volume back in volume polynomials. It is a strange and wonderful fact that Chow rings of matroids behave in many ways similarly to Chow rings of smooth projective varieties. Because of this, the Chow ring of a matroid is determined by a homogeneous polynomial called its volume polynomial, whose coefficients record the degrees of all possible top products of divisors. The use of the word "volume" is motivated by the fact that the volume polynomial of a smooth projective toric variety actually measures the volumes of certain polytopes associated to the variety. In the matroid setting, on the other hand, no such polytopes exist, and the goal of our work was to find more general polyhedral objects whose volume is measured by the volume polynomials of matroids. In this talk, I will motivate and describe these polyhedral objects. Parts of this work are joint with Jeshu Dastidar and Anastasia Nathanson.
Tuesday, February 9, 2021
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Nathan Ilten
Simon Frase University
TBA TBA
Tuesday, Febraury 16, 2021
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Brian Collier
UC Riverside
Global Slodowy slices for moduli spaces of Higgs bundles and holomorphic connections. Part 1. TBA
Tuesday, February 23, 2021
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Brian Collier
UC Riverside
Global Slodowy slices for moduli spaces of Higgs bundles and holomorphic connections. Part 2. TBA
Tuesday, March 2, 2021
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
TBA
TBA
TBA TBA
Tuesday, March 9, 2021
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Matthew Satriano
University of Waterloo
TBA TBA



Fall 2020

 
Date Speaker Title Abstract
Tuesday, October 13, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Patricio Gallardo
UC Riverside
On wonderful blow-ups. Techniques for constructing good compactifications of an open set is one of the main problems within Algebraic Geometry. In this talk, I will describe a tool known as Wonderful Compactifications due to Li-Li which generalizes earlier work by De Concini-Procesi on hyperplane arrangements. Applications to moduli problems will be described as well.
Tuesday, October 20, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Patricio Gallardo
UC Riverside
On wonderful blow-ups (second part). We will continue describing the theory of wonderful blow-ups. A particular focus is given to applications within moduli theory as well as open problems.
Tuesday, October 27, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Benjamin Schmidt
Leibniz Universität Hannover
A curious moduli space on cubic threefolds. The intermediate Jacobian J(X) of a cubic threefold X was introduced by Clemens and Griffiths in 1972 to prove irrationality of cubic threefolds. It is an abelian variety that can be thought of as parametrizing degree zero cycles in dimension one up to rational equivalence. In this talk we will concentrate on its theta divisor ϴ. Clemens and Griffiths proved the so-called Torelli theorem for cubic threefolds that says that the pair (J(X),ϴ) determines the cubic threefold. Shortly after, Mumford pointed out that X can be recovered just from the singularities of the theta divisor. In fact, it has a unique singularity whose tangent cone is the affine cone of the cubic X. Blowing the singularity up yields a resolution of singularities. We will construct this resolution as a moduli space of rank three vector bundles. This allows us to recover the so-called derived Torelli theorem. It roughly says that a certain triangulated subcategory (called the Kuznetsov component of X) of the bounded derived category of coherent sheaves determines X.
Tuesday, November 3, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
US Election Day
Election Day. No seminar meeting on US Election Day.
Tuesday, November 10, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Olivia Dumitrescu
University of North Carolina at Chapel Hill
Lagrangian correspondence between Hitchin and de Rham moduli spaces. In 2008 Simpson conjectures the existence of a holomorphic Lagrangian foliation in the de Rham moduli space of holomorphic G-connections for a complex reductive group G. The purpose of the talk is to establish the existence of a holomorphic Lagrangian foliation in the de Rham moduli space of holomorphic SL_2(C)-connections defined on a smooth connected projective curve C of genus at least 2. The conjectural holomorphic Lagrangian foliation does not seem to constitute a holomorphic Lagrangian fibration. I will present an algebraic geometry description of the Lagrangian correspondence of conformal limits, based on the work of Simpson. This talk is based on joint work with Jennifer Brown and Motohico Mulase.
Tuesday, November 17, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Dagan Karp
Harvey Mudd College
The Chow ring of heavy/light Hassett spaces via tropical geometry. Hassett spaces in genus 0 are moduli spaces of weighted pointed stable rational curves; they are important in the minimal model program and enumerative geometry. We compute the Chow ring of heavy/light Hassett spaces. The computation involves intersection theory on the toric variety corresponding to a graphic matroid, and rests upon the work of Cavalieri-Hampe-Markwig-Ranganathan. This is joint work with Siddarth Kannan and Shiyue Li.    Slides
Tuesday, November 24, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Antonio Laface.
University of Concepcion
Blown-up toric surfaces with non-polyhedral effective cone. I will discuss examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudoeffective cone, both in characteristic 0 and in positive characteristic. As a consequence, the pseudo-effective cone of the Grothendieck-Knudsen moduli space M0,n is not polyhedral for n ≥ 10 in characteristic 0 and for an infinite set of primes of positive density in positive characteristic.
Tuesday, December 1, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Javier Gonzalez-Anaya
UC Riverside
Negative curves in blowups of weighted projective planes. Blowups of toric varieties at general points have played a central role in many recent developments concerning the birational geometry of some moduli spaces. As part of this ongoing program, we'll discuss what is known about the Mori dream space property for blowups of weighted projective planes at a general point. By a result of Cutkosky, such a variety is a Mori dream space if and only if it contains two non-exceptional irreducible curves disjoint from each other; one of them having non-positive self-intersection. Such a curve a is called a “negative curve”. Negative curves largely govern the Mori dream space property for these varieties. In this talk I will survey what is currently known about their existence, how they "interact" with each other and how these interactions inform us about the Mori dream space property in many cases.
Tuesday, December 8, 2020
Start: 11:00 AM
Location: Online via Zoom (Please email the organizers if interested.)
Bernt Ivar Utstøl Nødland
Norwegian Defence Research Establishment
Cox rings of projectivized toric vector bundles. A toric vector bundle is a torus equivariant vector bundle on a toric variety. To a toric vector bundle one can associate a collection of lattice polytopes called the parliament of polytopes. We show how we can use these polytopes to give a description of the Cox ring of a projectivized toric vector bundle.