Calf Seminar
About the Calf
Calf is the junior COW, an algebraic geometry seminar group primarily aimed at PhD students.
The organisers for academic year 2022/23 are, Girtrude Hamm (Nottingham), James Jones (Loughborough), and Patrick Kennedy-Hunt (Cambridge), as well as an extensive network of local organisers at different universities. Calf announcements are made using the COW mailing list. If you would like to get involved in the organisation, or suggest your institution as the next venue, please contact any of the people named above.
The COW seminar has some funding for travel expenses, and information on reimbursement can be found on the main COW webpage.
About the Calf
Calf is the junior COW, an algebraic geometry seminar group primarily aimed at PhD students.
The organisers for academic year 2022/23 are, Girtrude Hamm (Nottingham), James Jones (Loughborough), and Patrick Kennedy-Hunt (Cambridge), as well as an extensive network of local organisers at different universities. Calf announcements are made using the COW mailing list. If you would like to get involved in the organisation, or suggest your institution as the next venue, please contact any of the people named above.
The COW seminar has some funding for travel expenses, and information on reimbursement can be found on the main COW webpage.
Recent Meeting:
Imperial College London 8th September 2023
Room 139, Huxley building
1:00pm: Erroxe Etxabarri Alberdi (University of Nottingham)
Title: Fano 3-folds with 1-dimentional K-moduli
Abstract: We give a friendly introduction to K-stability, and the motivation behind it. We will see how to study and completely describe all one-dimensional components of the K-moduli of smooth Fano 3-folds. And we will finish giving some specific examples for family 3.12. This result is in collaboration with Abban, Cheltsov, Denisova, Kaloghiros, Jiao, Martinez-Garcia and Papazachariou.
2:30pm: Simen Moe (Imperial College London)
Title: Stable rationality of polytopes
Abstract: Stable rationality specializes in smooth families, as shown by Nicaise--Shinder. Using toric geometry to construct degenerations, Nicaise--Ottem provided new examples of stably irrational hypersurfaces in projective space, such as very general quartic fivefolds. Their strategy uses the motivic volume as a stable birational invariant. However, this requires controlling the stable birational type of the strata in the degeneration. This can be obtained, for example, if a stratum has a strong type of variation of stable birational type. In this context, I will describe a large class of hypersurfaces in algebraic tori that exhibit a strong type of variation of stable birational types. This leads to a purely combinatorial strategy for proving the non-stable rationality of hypersurfaces in tori. As an application, I will discuss many new examples of stably irrational hypersurfaces in projective space.
4:00pm: Flora Poon (University of Bath)
Title: Kuga-Satake varieties of families of K3 surfaces of Picard rank 14
Abstract: In the 60s, Kuga and Satake constructed a weight one Hodge structure from a weight two Hodge structure of K3 type, which gives us a polarised abelian variety called the Kuga-Satake (KS) variety associated to a lattice polarised K3 surface. In the project, we study the KS varieties associated to K3 surfaces polarised by lattices of rank 14. Specifically, we have constructed the simple abelian subvarieties in the KS varieties associated to K3 surfaces in three special families, and discovered that they are dense in some moduli spaces of polarised abelian 8-folds of PEL type. We believe the dominant map we found from moduli spaces of K3 surfaces of Picard rank 14 to that of the simple factors of the associated KS varieties demonstrates how the type II_4 locally symmetric domains are associated to the type IV_6 ones.
Imperial College London 8th September 2023
Room 139, Huxley building
1:00pm: Erroxe Etxabarri Alberdi (University of Nottingham)
Title: Fano 3-folds with 1-dimentional K-moduli
Abstract: We give a friendly introduction to K-stability, and the motivation behind it. We will see how to study and completely describe all one-dimensional components of the K-moduli of smooth Fano 3-folds. And we will finish giving some specific examples for family 3.12. This result is in collaboration with Abban, Cheltsov, Denisova, Kaloghiros, Jiao, Martinez-Garcia and Papazachariou.
2:30pm: Simen Moe (Imperial College London)
Title: Stable rationality of polytopes
Abstract: Stable rationality specializes in smooth families, as shown by Nicaise--Shinder. Using toric geometry to construct degenerations, Nicaise--Ottem provided new examples of stably irrational hypersurfaces in projective space, such as very general quartic fivefolds. Their strategy uses the motivic volume as a stable birational invariant. However, this requires controlling the stable birational type of the strata in the degeneration. This can be obtained, for example, if a stratum has a strong type of variation of stable birational type. In this context, I will describe a large class of hypersurfaces in algebraic tori that exhibit a strong type of variation of stable birational types. This leads to a purely combinatorial strategy for proving the non-stable rationality of hypersurfaces in tori. As an application, I will discuss many new examples of stably irrational hypersurfaces in projective space.
4:00pm: Flora Poon (University of Bath)
Title: Kuga-Satake varieties of families of K3 surfaces of Picard rank 14
Abstract: In the 60s, Kuga and Satake constructed a weight one Hodge structure from a weight two Hodge structure of K3 type, which gives us a polarised abelian variety called the Kuga-Satake (KS) variety associated to a lattice polarised K3 surface. In the project, we study the KS varieties associated to K3 surfaces polarised by lattices of rank 14. Specifically, we have constructed the simple abelian subvarieties in the KS varieties associated to K3 surfaces in three special families, and discovered that they are dense in some moduli spaces of polarised abelian 8-folds of PEL type. We believe the dominant map we found from moduli spaces of K3 surfaces of Picard rank 14 to that of the simple factors of the associated KS varieties demonstrates how the type II_4 locally symmetric domains are associated to the type IV_6 ones.
This page is maintained by Chris Seaman.
