Seminar Algebra and Geometry - Spring 2019
| Date | Speaker | Title | Abstract |
|---|---|---|---|
| September 17 | (ETHZ) |
Automorphisms of rational surfaces | The starting point of this talk is a finite number of distinct points lying on an irreducible cubic curve in ℙ2 which we blow up to obtain a rational surface S. What conditions must the points satisfy such that a fixed element of the Weyl group associated to Pic(S) is realised as an automorphism of the surface S? I will discuss the conditions I worked on in my master thesis, present the relevant notions and results, and speak about the potential directions which could be further pursued. |
| September 23-27 | |||
| October 8 | (EPFL) |
On continuous automorphisms of Cremona groups | Julie Déserti showed that every automorphism of the plane Cremona group is inner up to a field automorphism of the base-field. In this talk we generalize this result to Cremona groups of arbitrary rank, however, only under the additional restriction that the automorphisms are also homeomorphisms with respect to the Zariski or the Euclidean topology on the Cremona group. We will consider similar questions for groups of polynomial automorphisms and groups of birational diffeomorphisms. This is joint work with Susanna Zimmermann. |
| October 15 | (Bern) |
ℚ-homology planes satisfying the Negativity Conjecture | A smooth complex normal algebraic surface S is a ℚ-homology plane if Hi(S,ℚ)=0 for i>0. This holds for example if S is a complement of a rational cuspidal curve in ℙ2. The Negativity Conjecture of K. Palka asserts that for a smooth completion (X,D) of S, κ(KX+½D)=-∞, so the minimal model of (X,½D) is a log Mori fiber space. Assume that S is of log general type, otherwise the geometry is well understood. It turns out that, as expected by tom Dieck and Petrie, all such S can be arranged in finitely many discrete families, each obtainable in a uniform way from certain arrangements of lines and conics on ℙ2. As a consequence, they all satisfy the Strong Rigidity Conjecture of Flenner and Zaidenberg; and all their automorphism groups are subgroups of S3. To illustrate this surprising rigidity, I will show how to construct all rational cuspidal curves (with complements of log general type, satisfying the Negativity Conjecture) inductively, by iterating quadratic Cremona maps. |
| October 22 | no talk |
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| October 29 | (Ioannina) |
Graded Rings and Birational Geometry | Un projection theory, initiated by Miles Reid, aims to construct and analyze complicated commutative rings in terms of simpler ones. It can also be considered as an algebraic language for birational geometry. The main purpose of the talk is to give a short introduction to the theory and describe some of its applications. |
| November 5 | (Rennes) |
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| November 12 | (Imperial College) |
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| November 18-20 | |||
| November 26 | (Munich) |
tba | |
| December 3 | (Loughbourough) |
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| December 10 | (Neuchâtel) |
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| December 17 |