Oberseminar Algebraische und Komplexe Geometrie im WiSe25/26

Von Mitte Oktober bis Ende Januar findet das Oberseminar Donnerstags von 14 bis 16 Uhr (Thursdays from 2:15 to 3:45 pm) statt. Vorträge dauern etwa eine Stunde; Nach dem Vortrag ist Zeit für Fragen und zum informellen Austausch mit dem Gast geplant. Der Raum ist IA1/63.

• 16. Okt. 2025: Giacomo Nanni (Ruhr-Universität Bochum, Università di Bologna):  Lagrangian fibrations on Nikulin orbifolds.

Abstract: The geometry of irreducible holomorphic symplectic (IHS, sometimes referred to as hyperkähler) manifolds can be studied through the numerical properties of algebraic classes with respect to a non-degenerate quadratic form on the second cohomology group. In this context, a famous conjecture (SYZ) predicts that the existence of Lagrangian fibrations is detected by the presence of certain isotropic classes. While the conjecture holds in all known examples, it remains open in general. Recently, singular analogues of IHS manifolds have been proposed, providing a new framework to test the conjecture in a singular setting. In this talk, I will focus on Nikulin orbifolds, which are among the simplest singular examples, and present recent work classifying possible fibrations in this deformation class, from which the SYZ conjecture follows in this specific case.

• 23. Okt. 2025: [POSTPONED] Christian Lehn (Ruhr-Universität Bochum): Introduction to currents and positivity concepts.

Abstract: We discuss basic properties of currents on a complex manifold such as positivity, Lelong numbers, Siu's theorem, and relation to positivity properties from algebraic geometry. 

• 6. Nov. 2025: Ludvig Modin (Leibniz-Universität Hannover): Moduli spaces for Θ-strata and non-reductive quotients.

Abstract: The U-hat theorem of Bérczi, Doran, Hawes and Kirwan gives conditions for when a linear action of a complex graded unipotent group admits a geometric quotient. It is one of the key results non-reductive geometric invariant theory is built on. We give a stacky re-interpretation of this theorem in terms of Θ-strata, as introduced by Halpern-Leistner, of algebraic stacks. As a corollary we generalize the U-hat theorem to not necessarily linear actions of graded unipotent groups over a Noetherian base scheme.

• 13. Nov. 2025: Jannik Wesner (TU Dortmund): Plane Quartics and their Associated Heptagons

  
  Abstract: For a convex polygon bounded by n lines there exists a unique curve -the so called adjoint- of degree n-3 passing through all intersection points of the lines except for those points, which are vertices of the polygon. Motivated by possible applications in finite element methods they were introduced by Wachspress in 1975 in his work on generalized barycentric coordinates. The definition of the adjoint extends to polygons in the complex projective plane, which are bounded by n lines in general position. The adjoint map, which maps an n-gon to its adjoint curve, happens to be dominant and generically finite only in the case of quartics and their associated heptagons. After establishing 864 by numerical certification as a lower bound, Kohn et al. (2021) conjectured this to be the precise number of heptagons associated to a generic plane quartic. In this talk, I will present joint work with Daniele Agostini, Daniel Plaumann and Rainer Sinn, which proves the conjecture: Employing intersection theory and the Scorza correspondence for quartics we show that 864 is indeed an upper bound. Furthermore we present a new proof for the lower bound revealed to us by a careful study of the Klein quartic.

• 27. Nov. 2025: Fateme Sajadi (University of Toronto). Zoom talk.
• 4. Dez. 2025: Simon Brandhorst (Universität des Saarlandes).
• 15. Jan. 2025:Matei Toma (Université de Lorraine).