## The Brussels-London Geometry Seminar

This is the webpage for the Brussels-London Geometry Seminar

The next seminar will take place online on Thursday 28 May 2020 at 13.15

### To sign up for this seminar, please complete this form.

Registration closes at 11:00 on Thursday 28th May

You will be sent a link to the Zoom meeting on Thursday morning

The Brussels-London Geometry Seminar, started in 2013 by Joel Fine and Jason Lotay, is a series of day-long seminars with three talks on a common theme in geometry. The series, made possible thanks to funding from the LMS, ERC and FNRS, has now reached its 20th edition. More information about this seminar series is available here.

Schedule for **Thursday 28 May 2020 **

13.15 | Start of meeting in Zoom. An opportunity to check your sound and vision. |

13.30 | Arend Bayer (Edinburgh) |

14.30 | Questions and short break |

14.45 | Margherita Lelli-Chiesa (Roma Tre) |

15.45 | Questions |

16.00 | Seminar closes |

**Margherita Lelli-Chiesa** (Roma Tre)

Title:* Genus two curves on abelian surfaces.*

Abstract:Let (S,L) be a general (d_1,d_2)-polarized abelian surfaces. The minimal geometric genus of any curve in the linear system |L| is two and there are finitely many curves of such genus. In analogy with Chen's results concerning rational curves on K3 surfaces, it is natural to ask whether all such curves are nodal. In the seminar I will prove that this holds true if and only if d_2 is not divisible by 4. In the cases where d_2 is a multiple of 4, I will construct curves in |L| having a triple, 4-tuple or 6-tuple point, and show that these are the only types of unnodal singularities a genus 2 curve in |L| may acquire. This is joint work with A. L. Knutsen.

**Arend Bayer** (Edinburgh)

Title:* Hyperkhaeler varieties from Fano varieties via stability conditions.*

Abstract:I will explain how to obtain (families of) Hyperkaehler varieties from (families of) some types of Fano varieties. The construction currently applies to cubic fourfolds, and Gushel-Mukai fourfolds. It goes via moduli spaces of stable objects for stability condition on their "Kuznetsov categories", a certain component of the derived category of these Fano varieties. This, for example, gives two infinite collections of locally complete unirational families of polarised Hyperkaehler varieties. Conversely, I will explain some applications to the geometry of cubic fourfolds.

## Previous Seminar

Thu 7 May 2020

**Baptiste Chantraine , **University of Nantes

Title:* Invariants of Legendrian submanifolds in non-coorientable contact structures*

**András Juhász, **University of Oxford

Title: *Transverse invariants and exotic surfaces in the 4-ball*

Zoom is the online platform being used to deliver this seminar series.

**This seminar series is supported as part of the ICMS/INI Online Mathematical Sciences Seminars. **