Boston Algebraic Geometry Day

Speakers:

Dawei Chen, Rob Lazarsfeld, Rosie Shen, Montserrat Teixidor i Bigas

Location: Harvard University Science Center 507

Schedule (titles and abstracts are below)

9:15-10:00.  Check-in and pastries/coffee
10:00-11:00.  Rosie Shen
11:00-11:30.  Coffee break
11:30-12:30.  Dawei Chen
12:30-2:30.  Lunch break
2:30-3:30.  Montserrat Teixidor i Bigas
3:30-4:00.  Coffee break
4:00-5:00.  Rob Lazarsfeld

Abstracts:

Dawei Chen (Boston College): Gorenstein singularities with C*-action and moduli spaces of holomorphic differentials

We associate to each holomorphic differential on a smooth curve a Gorenstein singularity with C*-action via a test configuration. This construction decomposes moduli spaces of differentials with prescribed orders of zeros into miniversal deformation spaces with good C*-action. As applications, we classify such singularities that arise in low genus, compute the invariants of the singularities in the log minimal model program of M_g, and study the geometry and topology for related moduli spaces. This is based on joint work with Fei Yu: arXiv:2507.09078.

Rob Lazarsfeld (Stony Brook): Birational complexity of algebraic varieties: some open questions

I will discuss some open problems loosely centered about how “complicated” a variety might be from a birational viewpoint. The talk will present numerous questions, but no answers.

Rosie Shen (Harvard): Higher Du Bois singularities and K-regularity

We explain how recent progress in higher Du Bois singularities leads to new results about K-regularity, a notion that measures the homotopy invariance of algebraic K-theory.

Montserrat Teixidor i Bigas (Tufts): Petri Loci

It is well known that for the generic curve of genus g and any line bundle, the Petri map is injective. Therefore the set of curves of genus g that have a $g^r_d$ for which the  Petri map is not injective is a proper subset of ${\mathcal M}_g$, which is expected to be a divisor. This is not always the case, so we can obtain subsets of ${\mathcal M}_g$ of higher codimension. We could ask for the Petri map not only to be non-injective but also to have a kernel of given dimension.  Similar questions are valid also for vector bundles of higher rank. We will discuss these question (but only a few answers).