Seminar on Stacks (PhD Seminar)
Termin: Montag 16-18 Uhr in WSC-S-U-3.01
Dozenten J. Heinloth
We will usually start the seminar with a discussion/Q&A/recap-session on one of the Thursday seminars.
Afterwards we discuss a topic/an article one of us wants to understand, the choice for the next topic is usually made at the end of the seminar.
The list below will thus be updated regularly, a list of links to articles and preprints discussed is included below.
| Date | Speaker | Titel |
|---|---|---|
| 07.04.2025 | AEI-DFG Workshop | Topology of moduli of G-Hodge bundles |
| 28.04.2025 | Jochen Heinloth | discussion session |
| 05.05.2025, 16:30 | Niklas Müller | Inequalities of Miyaoka-Yau-type & Uniformisation of Minimal Varieties of Intermediate Kodaira Dimension |
| 12.05.2025 | Diego Ruiz-Cases | Holomorphic structures on principal bundles for non-reductive structure groups |
| 19.05.2025 | discussion session on stability conditions | |
| 02.06.2025 | discussion session on non-reductive GIT | |
| 16.06.2025 | Felix Schremmer | Short talk on his work on affine Deligne-Lusztig varieties |
| 23.06.2025 | discussion | |
| 30.06.2025 | Michele Pernice | Moduli stacks of genus one Gorenstein curves with projective good moduli spaces |
| 07.07.2025 | N.N. | tba |
| 14.07.2025 | N.N. | tba |
Michele Pernice: Moduli stacks of genus one Gorenstein curves with projective good moduli spaces
The search for alternative compactifications of the moduli space of smooth curves has been central in the panorama of moduli spaces. A possible way to construct such compactifications is allowing curves with worse-than-nodal singularities in the moduli problem and imposing some stability conditions using the combinatorics of the curves to get the desired moduli space. We classify the open substacks inside the moduli stack $\mathcal{G}_{1,n}$ of $n$-pointed Gorenstein curves of genus one which admits a proper good moduli space. They agree with those defined by Bozlee, Kuo and Neff. Moreover, we will prove that these spaces are actually projective and we will explain why the classification is a consequence of a wall-crossing phenomenon. This is a on-going project with Luca Battistella and Andrea Di Lorenzo.
Links to Articles and Preprints for the different topics:
Notes on stacks and moduli (by Jarod Alper)