Center for Complex Geometry

Gebhard Martin, Automorphisms of del Pezzo Surfaces I
2024-03-05 11:00 - 12:00 (Asia/Seoul) | B236-1, IBS, Korea, Republic of
Speaker

Gebhard Martin
Universität Bonn

Motivated by the classification of finite subgroups of the Cremona group of the plane, I will survey old and new results on automorphism groups of del Pezzo surfaces. In particular, I will report on joint work with Igor Dolgachev on the classification of automorphism groups of smooth del Pezzo surfaces and on joint work with Claudia Stadlmayr on the classification of vector fields on mildly singular del Pezzo surfaces. Special emphasis will be placed on the theory of actions of infinitesimal group schemes and characteristic-free methods in classical algebraic geometry.

Claudia Stadlmayr, Which Rational Double Points Occur on del Pezzo Surfaces?
2024-03-07 15:30 - 16:30 | B236-1, IBS, Korea, Republic of
Speaker

Claudia Stadlmayr
Technische Universität München

Canonical surface singularities, also called rational double points (RDPs), can be classified according to their dual resolution graphs, which are Dynkin diagrams of types A, D, and E. Whereas in characteristic different from 2, 3, and 5, rational double points are “taut”, that is, they are uniquely determined by their dual resolution graph, this is not necessarily the case in small characteristics. To such non-taut RDPs Artin assigned a coindex distinguishing the ones with the same resolution graph in terms of their deformation theory. In 1934, Du Val determined all configurations of rational double points that can appear on complex RDP del Pezzo surfaces. In order to extend Du Val’s work to positive characteristic, one has to determine the Artin coindices to distinguish the non-taut rational double points that occur. In this talk, I will explain how to answer the question “Which rational double points (and configurations of them) occur on del Pezzo surfaces?” for all RDP del Pezzo surfaces in all characteristics. This will be done by first reducing the problem to degree 1 and then exploiting the connection to (Weierstraß models of) rational (quasi-)elliptic surfaces.

Gebhard Martin, Automorphisms of del Pezzo Surfaces II
2024-03-12 16:00 - 17:00 | B236-1, IBS, Korea, Republic of

Gebhard Martin, Automorphisms of del Pezzo Surfaces III
2024-03-14 15:30 - 16:30 | B236-1, IBS, Korea, Republic of

Boris Doubrov, Bifiltered Parabolic Geometries
2024-03-19 16:00 - 17:00 | B266, IBS, Korea, Republic of
Speaker

Boris Doubrov
Belarusian State University, Minsk

We introduce the notion of a bifiltered manifold and generalizing the constructions of the symbol and Tanaka prolongation from nilpotent differential geometry. Next, we consider bifiltered manifolds modeled by bigradings of simple Lie algebras and show how this generalizes known constructions in the parabolic geometries such as existence of a unique normal Cartan connection. Finally, we show how the language of bifiltered manifolds can be used for uniform treatment of correspondence spaces in parabolic geometries, where the covering space is not necessarily regular in the classical sense.

Dennis The, On 4D Split-conformal Structures with G2-symmetric Twistor Distribution
2024-03-21 16:00 - 17:00 | B266, IBS, Korea, Republic of
Speaker

Dennis The
The Artic University of Norway, Tromso

In their 2013 article, An & Nurowski considered two surfaces rolling on each other without twisting or slipping, and defined a twistor distribution (on the space of all real totally null self-dual 2-planes) for the associated 4D split-signature conformal structure. If this split-conformal structure is not anti-self dual, then the twistor distribution is a (2,3,5)-distribution, and An-Nurowski identified interesting rolling examples where it achieves maximal, i.e. G2, symmetry. Relaxing the rolling assumption, a similar construction can be made for any 4D split-conformal structure, and my talk will discuss a broader classification of examples where such exceptional symmetry for the twistor distribution is achieved. (Joint work with Pawel Nurowski & Katja Sagerschnig.)

Yong Hu, Noether Inequality for Irregular Threefolds of General Type
2024-03-26 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Yong Hu
Shanghai Jiao Tong University

Let X be a smooth irregular 3-fold of general type. In this talk, we will prove that the optimal Noether inequality vol(X) ≥ (4/3) pg(X) holds if pg(X) ≥ 16 or if X has a Gorenstein minimal model. Moreover, when X attains the equality and pg(X) ≥ 16, its canonical model will be explicitly described. This is a joint work with Tong Zhang.
