## Joint Seminar on Complex Algebraic Geometry and Complex Analysis

(Bochum - Essen - Köln - Wuppertal)

Photo by Max Greve and Timo Bobert
## The Seminar

The "Joint Seminar on Complex Algebraic Geometry and Complex Analysis" is a research seminar, organised by the algebraic and complex geometry research groups in Bochum, Essen, Cologne, and Wuppertal. The seminar meets roughly twice per semester for a full day in Bochum, Essen, Cologne, or Wuppertal. There are three talks per meeting, both by invited guests and by speakers from the organising universities. We aim to leave ample room for discussions.

The talks are open for everyone. Contact one of the organisers if you are interested in attending the meeting. We have some funds that might help to support travel for some junior participants.

Meetings of the seminar are partially supported by

- SFB/TR 45 "Periods, moduli spaces and arithmetic of algebraic varieties"
- SFB/TR 191 "Symplectic structures in geometry, algebra and dynamics"

## Next Meeting

### DATE AND PLACE

The next meeting will take place on **Friday, January 18th, 2019** in **Essen**.

### TALKS

**André Belotto (Marseille):**Resolution of singularities of the cotangent sheaf of a singular variety

Abstract:

The subject of the talk is resolution of singularities of differential forms on an algebraic or analytic variety. We address the problem of finding a resolution of singularities $\sigma: X \to X_0$ of a singular algebraic or analytic variety $X_0$ such that the pulled back cotangent sheaf of $X_0$ (i.e., the pull-back of the Kahler differential forms) is given, locally in $X$, by monomial differential forms (with respect to a suitable coordinate system). In a work in collaboration with Bierstone, Grandjean and Milman, we give a positive answer to the problem when $dim X_0\leq 3$. The result was previously known for surfaces with isolated singularities (Hsiang-Pati 1985, Pardon-Stern 2001). Consequences include monomialization (up to local bi-Lipschitz equivalence) of the inner metric of a complex projective variety $X_0$; there have been important applications of the latter to L2-cohomology. We will also discuss a characterization of the problem in terms of (logarithmic) Fitting ideals.**Andreas Höring (Nice):**Pseudoeffective thresholds for polarised Hyperkähler manifolds

Abstract:

Let $X$ be a complex projective manifold that is Hyperkähler. By a recent result of Thomas Peternell and myself the cotangent bundle of $X$ is not pseudoeffective. One way to mesure this negativity more precisely is to give sufficient conditions for the twist $\Omega_X \otimes A$ to be pseudoeffective if $A$ is some ample line bundle. I will report on work in progress with Fabrizio Anella : for Hyperkähler manifolds of type $K3^n$, we give a sufficient condition that depends only on the Segre classes/Beauville form of $X$. For K3 surfaces this sufficient condition is necessary for infinitely many families. In the talk I will explain all the terminology appearing in this abstract.**Valdemar Tsanov (Bochum):**On the degrees of generating invariants

Abstract:

The ring of invariant polynomials $\mathbb{C}[V]^{G}$ on a given finite dimensional representation space of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being nonconstructive, the generators and their degrees have remained a subject of interest. In this talk I will derive certain divisors of the degrees of the generators. Also, for irreducible representations, I will derive lower bounds for the degrees, determined by the geometric properties of the unique closed projective $G$-orbit and its secant varieties. For certain special classes of representations, there is an exact correspondence between the generators and the secant varieties intersecting the semistable locus.

### SCHEDULE

**10:30 - 11:30 ** Tsanov

**11:45 - 12:45 ** Höring

**12:45 - 14:30 ** Lunch break

**14:30 - 15:30 ** Belotto

### VENUE

Universität Duisburg-Essen

Fakultät für Mathematik

Weststadt-Carrée, Essen

All talks will take place in the

**meeting room on the fifth floor**.

How to find the seminar room: see the maps on the following website.

## Organisers

Kevin Fritsch

Ruhr-Universität Bochum

kevin [dot] fritsch [at] rub [dot] de

Daniel Greb

Universität Duisburg-Essen

daniel [dot] greb [at] uni-due [dot] de

George Marinescu

Universität zu Köln

gmarines [at] math [dot] uni-koeln [dot] de

Jean Ruppenthal

Bergische Universität Wuppertal

jean [dot] ruppenthal [at] math [dot] uni-wuppertal [dot]de

## Past Meetings

**26.4.2013, Bochum:** Tim Kirschner, Christian Miebach, Henrik Seppänen

**28.6.2013, Wuppertal:** Rafael Andrist, Immanuel Stampfli, Matei Toma

**22.11.2013, Bochum:** Sébastien Boucksom, Egmont Porten, Sönke Rollenske

**24.1.2014, Wuppertal:** Clemens Jörder, Helge Ruddat, Jörg Winkelmann

**16.5.2014, Bochum:** Alberto Abbondandolo, Judith Brinkschulte, Julius Ross

**20.6.2014, Wuppertal:** Julie Déserti, Slawomir Dinew, Slawomir Rams

**24.10.2014, Bochum:** Henri Guenancia, Shulim Kaliman, Adriano Tomassini

**15.12.2014, Wuppertal:** Richard Lärkäng, Christian Miebach, Marco Spinaci

**7.5.2015, Essen:** Brent Doran, Erwan Rousseau, Emanuel Scheidegger

**15.6.2015, Bochum:** Roya Beheshti, Daniel Greb, Hossein Raufi

**27.11.2015, Wuppertal:** Francesco Bei, Kai Cieliebak, Tyson Ritter

**1.2.2016, Essen:** Ursula Ludwig, George Marinescu, Wenhao Ou

**25.4.2016, Wuppertal:** Gian Maria Dall’Ara, Christian Lehn, Luca Tasin

**26.6.2016, Cologne:** Chin-Yu Hsiao, Stefan Nemirovski, Nikhil Savale

**25.11.2016, Bochum:** Ana-Maria Brecan, Antonio di Scala, Dan Popovici

**27.1.2017, Essen**: Tim Kirschner, Viêt Anh Nguyên, Stefan Schreieder

**21.4.2017, Wuppertal**: Vicente Cortés, Philipp Naumann, Markus Reineke

**7.7.2017, Cologne**: Roger Bielawski, Dan Coman, Martin Schwald

**3.11.2017, Bochum**: Junyan Cao, Sönke Rollenske, Robert Szöke

**1.2.2018, Essen**: Gilberto Bini, Ruadhaí Dervan, Hendrik Herrmann

**27.4.2018, Wuppertal**: Hugues Auvray, Bernd Stratmann, Michael Lennox Wong

**6.7.2018, Cologne**: Turgay Bayraktar, Jarek Buczynski, Andrew Dancer

**23.11.2018, Bochum**: Ben Anthes, Kevin Fritsch, Ariyan Javanpeykar