Bernd Sturmfels: Quartic Curves and their Bitangents

Bernd Sturmfels, University of California Berkeley

Time: Wed 2011-02-02 16.00

Location: Room 3721, Department of Mathematics, KTH, Lindstedtsvägen 25, 7th floor

A smooth quartic curve in the complex projective plane has 36 inequiva- lent representations as a symmetric determinant of linear forms and 63 repre- sentations as a sum of three squares. These correspond to Cayley octads and Steiner complexes respectively. We present exact algorithms for computing these objects from the 28 bitangents. This expresses Vinnikov quartics as spectrahedra and positive quartics as Gram matrices. We explore the geom- etry of Gram spectrahedra and we find equations for the variety of Cayley octads. Interwoven is an exposition of much of the 19th century theory of plane quartics.

Kollokvier 2011

Titel Datum
Wendelin Werner: Random surfaces, random geometries 2011‑12‑14
Ragni Piene: The problematic art of counting 2011‑11‑16
Günter M. Ziegler: On some partition problems and their configuration spaces 2011‑10‑12
Carles Broto: Local aspects of groups and loop spaces 2011‑05‑11
Bernd Sturmfels: Quartic Curves and their Bitangents 2011‑02‑02