# GV invariants in non-toric local CY threefolds, some of which do not have compact curves (Andrés COLLINUCCI, Brussels University)

31.10.2024 16:00

Local Calabi-Yau singularities are a playground for counting BPS states, and indeed, for toric varieties, the techniques such as the topological vertex, for computing Gopakumar-Vafa invariants are very powerful.

There is, however, an interesting class of *non-toric* CY local threefolds, of which the conifold is a special case, that are constructed as ALE fibrations over the complex plane. They are known as higher-length flops.

For those cases, my collaborators and I have stumbled upon a new duality frame that allowed us to compute GV invariants independently of previously known methods.

In this talk, I will explain the concept of “simultaneous partial resolutions”, which is a group-theoretic way of building such threefolds.

I will then show, that M-theory on such geometries can be dualized to IIA with intersecting D6-branes, where the GV invariants translate to elementary open string Ext^1 computations.

Finally, I will present some results for CY threefolds that do not admit crepant resolutions. In this case, we are essentially giving a new definition of GV invariants for threefolds that do not have compact curves.

### Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Physical Mathematics Seminar"

### Organisé par

Section de mathématiques### Intervenant-e-s

Andrés Collinucci, Brussels Universityentrée libre