Loading Events

« All Events

  • This event has passed.

Fabrizio Catanese, [IBS-KAIST Seminar] Geometry and Dynamics of Geometric Endomorphisms of the Hesse Moduli Space of Elliptic Curves

September 8 @ 11:00 am - 12:00 pm KST

B236-1, IBS Korea, Republic of


Fabrizio Catanese
University of Bayreuth

We consider the geometric map C, called Cayleyan, associating to a plane cubic E the adjoint of its dual curve. We show that C and the classical Hessian map H generate a free semigroup. We begin the investigation of the geometry and dynamics of these maps, and of the geometrically special elliptic curves: these are the elliptic curves isomorphic to cubics in the Hesse pencil which are fixed by some endomorphism belonging to the semigroup generated by H, C. We point out how the dynamic behaviours of H and C differ drastically. Firstly, concerning the number of real periodic points: for H these are infinitely many, for C they are just 4. Secondly, the Julia set of H is the whole projective line, unlike what happens for all elements of the semigroup which are not iterates of H.


September 8
11:00 am - 12:00 pm KST
Event Category:
Event Tags:


IBS Korea, Republic of


Jaehyun Hong
IBS 복소기하학연구단 Center for Complex Geometry
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
Copyright © IBS 2020. All rights reserved.