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Fachbereich
Institut für Mathematik
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Oberseminar Algebra und Geometrie

Termin und Ort:


Veranstalter: Algebra und Geometrie

Oberseminar Algebra und Geometrie

Apr 29 2026
16:00

Robert-Mayer-Str. 6-8, Raum 308 

Michael Temkin (MPI Bonn): Wild Hurwitz spaces and level structures

Abstract: Hurwitz moduli spaces of covers of curves of degree d are classical and well studied objects if one assumes that d! is invertible and hence no wild ramification phenomena occur. There were very few attempts to study the wild case. In the most important one Abramovich and Oort started with the classical space H_{2,1,0,4} of double covers of P^1 ramified at four points and (following an idea of Kontsevich and Pandariphande) described its schematic closure H in the space of stable maps over Z. The result over F_2 was both strange and informative, but lacked a modular interpretation.

In the first part of my talk I will describe the example of Abramovich-Oort and then tell about a work in progress of Hippold, where a (logarithmic) modular version of compactified Hurwitz space of degree p is constructed when only (p-1)! is invertible. In particular, this conceptually explains phenomena observed by Abramovich-Oort. In the second part I will describe another outcome of the same ideas. It was observed by Abramovich-Oort that H is the blowing up of the modular curve X(2). This is not a coincidence, and the same ideas can be used to refine the wild level structures of Drinfeld and construct modular interpretation of the minimal modifications of the curves X(p^n) which separate ordinary branches at any supersingular point. This is a very recent work in progress and the precise description of the obtained spaces is still to be found.

Oberseminar Algebra und Geometrie

Apr 16 2026
16:15

Robert-Mayer-Str. 6-8, Raum 309

Valeria Bertini (Universita degli Studi di Milano) : Quotients of Hyperkähler manifolds

Abstract: Hyperkähler manifolds have been intensively studied from the 80s on, being building blocks of compact Kähler manifolds with trivial first Chern class; despite their natural role, finding examples of Hyperkähler manifolds is well known to be extremely challenging. In recent years, the focus has turned on their singular analogue, appearing naturally from the birational geometry perspective, and finally giving many new families of examples. A successful technique to produce singular examples is to consider (terminalizations of) quotients of smooth Hyperkähler manifolds. In this talk I will start presenting some recent results on singular Hyperkähler varieties constructed as quotients, and then I will turn to the case the quotient is a Calabi-Yau variety. The first part is a joint work with Grossi, Mauri and Mazzon, and the second one is work in progress with Garbagnati.