Humboldt Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik

Forschungsseminar "Algebraische Geometrie"

Wintersemester 2016/17

Das Forschungsseminar findet mittwochs in der Zeit von 15:00 - 17:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 2.006 (Haus 2, Erdgeschoss), statt.

Seminar: Algebraic Geometry an der FU

19.10.2016 kein Seminar
26.10.2016 Hsueh-Yung Lin (HU Berlin)
Title: Bimeromorphic Kodaira problem for non-uniruled Kähler 3-folds

Abstract: The bimeromorphic Kodaira problem asks whether a compact Kähler manifold has a bimeromorphic model which is deformation equivalent to a projective variety. After giving a survey of known results and introducing Kähler 3-folds from the point of view of the minimal model program, we will focus on compact Kähler 3-folds of Kodaira dimension 1, and show that the bimeromorphic Kodaira problem has a positive answer for these manifolds. Together with earlier work of N. Nakayama and recent work of P. Graf, we answer positively the bimeromorphic Kodaira problem for non-uniruled Kähler 3-folds, as predicted by a conjecture of T. Peternell.
02.11.2016 Marian Aprodu (University of Bucharest)
Title: Syzygies and secant loci

Abstract: We discuss the interactions between syzygies of curves and the geometry of the secant loci in the symmetric products. We show that a regular behavior of these loci for special line bundles imply the vanishing of linear syzygies. The talk is based on a joint work with Edoardo Sernesi.
09.11.2016 Alessandro Verra (Universita di Roma Tre)
Title: Rational parametrizations of universal K3 surfaces of low genus via cubic fourfolds.

Abstract: In complex projective geometry the interplay between K3 surfaces and cubic fourfolds is a well known topic, related to the rationality problem for these fourfolds. In the talk a survey on the topic and its recent results is given. Then special cases of interest are studied. One is the family of conjecturally rational cubic fourfolds X containing a 3-nodal rational scroll R of degree 7. This family is associated to the moduli F 14 of genus 14 K3 surfaces. The following new result is presented: the moduli space of pairs (X, R) is rational and birational to the universal K3 over F 14. The method applies to the next case to be considered, namely the space of moduli of pairs (X, R) such that R is an 8-nodal rational scroll. In this case the unirationality of this space, and hence of the universal K3 surface of genus 42, can follow.
16.11.2016 Rahul Pandharipande (ETH Zürich)
Title: The r-spin CohFT for higher r

Abstract: I will discuss the Cohomological Field Theory obtained from the r-spin class on the moduli space of r-spin curves for higher r. Exact calculations can be made at particular semisimple points. The results include exact formulas for r-spin correlators in genus 0, useful families of tautological relations in higher genus, and a surprising connection to the moduli of holomorphic differentials. The talk represents joint work with F. Janda, A. Pixton, and D. Zvonkine.
23.11.2016 Kay Rülling (HU Berlin)
Title: t.b.a.

Abstract: t.b.a.
30.11.2016 (Raum 0'101, Erwin-Schrödinger-Zentrum) Joint seminar in algebraic geometry with the Sturmfels group from Leipzig/Berlin
13:30 - 14:30 Bernd Sturmfels (U Berkeley/U Leipzig)
15:15 - 16:15 Igor Dolgachev (U Michigan)
Title: t.b.a.

Abstract: t.b.a.
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