Search Research Symposium Abstracts

Rationality of conic bundle threefolds over non-closed fields

A variety over a non-closed field is said to be geometrically rational if it becomes birationally equivalent to projective space after base changing to an algebraic closure. If a variety is geometrically rational, one can ask whether it is also rational over the original ground field. We study the rationality question for geometrically rational conic bundle [Read More...]

Presenter: Lena Ji, University of Michigan
Authors: Lena Ji, Sarah Frei, Soumya Sankar, Bianca Viray, and Isabel Vogt
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 10:15 am

Cubic Fourfolds with an Involution

Cubic fourfolds are one of the most intensely studied objects in Algebraic Geometry, especially due to their role in the construction of hyperkähler manifolds. A big open problem surrounding hyperkähler manifolds is the construction of new examples: currently there are only 4 known deformation types. One approach is to consider finite symplectic group [Read More...]

Presenter: Lisa Marquand, Stony Brook University
Authors: Lisa Marquand
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 10:40 am

A New Characterization of the Deligne-Du Bois Complex

Many singularities appearing in higher dimensional geometry are Du Bois. This is especially true in moduli theory, where Du Bois singularities play a key role. In this talk, we will examine known characterizations of Du Bois singularities and introduce a hyperresolution-free characterization of the entire Deligne-Du Bois [Read More...]

Presenter: Kristine Hampton, University of Washington
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 11:05 am

Kodaira dimension of some moduli spaces of hyperkähler manifolds

We study some moduli spaces of polarized hyperkähler manifolds of K3 type. We use techniques of Gritsenko-Hulek-Sankaran involving modular forms to give lower bounds on the degree of the polarization after which the moduli space is always of general [Read More...]

Presenter: Laure Flapan, Michigan State University
Authors: Ignacio Barros, Pietro Beri, Emma Brakkee, Laure Flapan
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 11:30 am

Monodromy of Tamely Ramified Covers of Curves*

The étale fundamental group $\pi_1^{et}$ in algebraic geometry formalizes an analogy between Galois theory and topology, extending our intuition to spaces in which loops, as defined traditionally, do not yield meaningful information. For a curve $X$ over an algebraically closed field of characteristic $0$, finite quotients of $\pi_1^{et}$ can be described [Read More...]

Presenter: Renee Bell, University of Pennsylvania
Authors: Renee Bell, Jeremy Booher, Will Chen, Yuan Liu
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 3:20 pm

K-rings of wonderful varieties and matroids

Chow rings of wonderful varieties and matroids have played key roles in solving many long-standing open questions in combinatorics and algebraic geometry. We study the K-rings of wonderful varieties associated with realizable matroids, as deformations of the Chow rings. We also compute the Euler characteristic of every line bundle on wonderful varieties, [Read More...]

Presenter: Shiyue Li, Brown University
Authors: Matt Larson, Shiyue Li, Sam Payne, Nicholas Proudfoot
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 3:45 pm

Symplectic involutions of hyperkahler fourfolds of Kummer type

The middle cohomology of hyperkahler fourfolds of Kummer type was studied by Hassett and Tschinkel, who showed that a large portion is generated by cycle classes of fixed loci of symplectic involutions. In recent joint work with Katrina Honigs, we study hyperkahler fourfolds over arbitrary fields which are constructed as fibers of the Albanese map on moduli [Read More...]

Presenter: Sarah Frei, Rice University
Authors: Sarah Frei, Katrina Honigs
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 4:10 pm

Higher Fano manifold

Fano manifolds are complex projective manifolds having positive first Chern class. The positivity condition on the first Chern class has far reaching geometric and arithmetic implications, making Fano manifolds a central subject in modern algebraic geometry. For instance, Fano manifolds are covered by rational curves, and families of Fano manifolds over one [Read More...]

Presenter: Kelly Jabbusch, University of Michigan - Dearborn
Authors: Carolina Araujo, Roya Beheshti, Ana-Maria Castravet, Kelly Jabbusch, Svetlana Makarova, Enrica Mazzon, Libby Taylor and Nivedita Viswanathan
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 4:35 pm