Northern German Algebraic Geometry Seminar

Speakers

Gregorio Baldi (Jussieu) Anna Cadoret (Jussieu) Salvatore Floccari (Bielefeld) Jan Lange (Hanover)

Angela Ortega (Berlin) Thomas Peternell (Bayreuth) Alessandra Sarti (Poitiers)

Organisers

Ana Botero

Eike Lau

Charles Vial

NoGAGS

The Northern German Algebraic Geometry Seminar is a regular joint seminar of the algebraic geometry groups in Berlin, Bielefeld, Goettingen, Groningen, Hamburg, Hanover, Leipzig, Münster and Oldenburg. Information on the previous meetings can be found here.

Schedule

There will be a dinner on Thursday evening and we kindly ask participants to register for it. (Unfortunately, we will not be able to cover the dinner costs for participants).
Thursday:
10:30-11:00 Registration
11:00-12:00 Sarti 
12:00-13:00 Floccari
13:00-14:00 Lunch break
14:00-15:00 Baldi
15:00-16:00 Coffee break
16:00-17:00 Cadoret
Friday:
09:00-10:00 Ortega
10:00-10:45 Coffee break
10:45-11:45 Lange
11:45-12:45 Peternell

Registration

In order to organise badges, coffee breaks, and the conference dinner, we ask participants to register before 15 January 2025 by sending an email to Claudia Gaertner cgaertner@math.uni-bielefeld.de with their name and affiliation, and whether they intend to attend dinner.

Abstracts

Gregorio Baldi
Title: The Noether-Lefschetz locus and the questions of Harris and Voisin
Abstract: After recalling the classical results on the distribution of the components of the NL locus from the 80s and early 90s, I will explain how they relate to the "completed Zilber-Pink philosophy" developed with B. Klingler and E. Ullmo. Armed with this viewpoint, we will show that the so called exceptional components are not Zarsiski dense in the moduli space of smooth surfaces of degree d. The novelty is that they, in some sense, they are explained by the presence of extra ‘’higher Hodge tensors’’. If time permits, I will sketch a new proof of this result (joint with D. Urbanik), which builds on Galois theory of foliations.

Anna Cadoret
Title: Variation of Tannaka group of perverse sheaves over abelian varieties in families (Joint with Haohao Liu)
Abstract: Given a relative perverse sheaf P (in the sense of Hansen-Scholze) over an abelian scheme A/S over a smooth irreducible variety S, whose restriction to the geometric generic fiber A_\eta is semisimple (in the corresponding Tannakian category), we prove that the loci of all s in S where the connected component of the derived subgroup of the Tannaka group of P restricted to A_s degenerates is not Zariski-dense. This builds on and enhances previous works by Kramer and Weissauer.

Salvatore Floccari
Title: The hyperKummer construction
Abstract: Any hyperKähler manifold K of Kum^3-type has a naturally associated manifold Y_K of K3^[3]-type, defined as crepant resolution of the quotient K/G by the action of a finite group G=(Z/2)^5. I will report on joint work with Lie Fu in which we explore this hyperKummer construction guided by the analogy with the classical Kummer construction in dimension 2. We obtain a birational characterization of hyperKummer varieties of K3^[3]-type as well as relations between K and Y_K at the level of motives and derived categories. As I will explain, our study suggests to construct very general projective varieties of Kum^3-type as rational covers of suitable moduli spaces of sheaves on certain K3 surfaces. If time permits, I will also discuss a somewhat surprising relation with certain hyperKähler varieties of OG6-type.

Jan Lange
Title: On the rationality problem for hypersurfaces
Abstract: We prove that a very general hypersurface of degree $d \geq 4$ and dimension at most $(d+1)2^{d-4}$ does not admit a decomposition of the diagonal, in particular it is neither stably nor retract rational nor $\mathbb{A}^1$-connected. This joint work with Stefan Schreieder improves earlier results by Schreieder (2019) and Moe (2023).

Angela Ortega
Title: Families of simple Jacobians with many automorphisms
Abstract: We consider a (2g-1)-dimensional family of Jacobians of dimension (d-1)(g-1)/2 arising as quotient of curves of unramified cyclic coverings of prime degree d > 2 over hyperelliptic curves of genus g. We proved that the generic element in this family is simple by means of a deformation argument and described completely its endomorphism algebra. I will also explain how to use this result to show that the Prym map corresponding to the cyclic covering is generically injective under some mild numerical restrictions on d and g. This is a joint work with J.C. Naranjo, G.P. Pirola and I. Spelta.