Algebraic Geometry Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Algebraic Geometry Group, Department of Mathematics
- Location
- 207 Psychology Building
- Date
- Nov 18, 2025 3:00 pm
- Speaker
- Miguel Moreira (Massachusetts Institute of Technology)
- Views
- 23
- Originating Calendar
- Algebraic Geometry Calendar
Title: Chern filtration on moduli of 1-dimensional sheaves
Abstract: Gopakumar-Vafa, mathematically defined by Maulik and Toda, are invariants of Calabi-Yau 3-folds that are conjectured to match other curve counting theories, such as Gromov-Witten and stable pairs, and explain their integrality properties. Their definition becomes more concrete, even though still a great challenge to calculate, in the case of local del Pezzo surfaces; there, GV invariants can be extracted from the perverse filtration on the cohomology of smooth moduli spaces. I will explain the construction of a different filtration, called the Chern filtration, which we conjecture to match the perverse one. I will discuss what is known and expected about the Chern filtration, including some assymptotic formulas for its graded dimensions, a vanishing result and a new perspective on chi-independence. This is based on joint work with W. Lim and W. Pi.