Type: Seminar

Distribution: World

Expiry: 12 Apr 2012

Auth: zhangou@bari.maths.usyd.edu.au

Speaker: Prof. Alexandru Dimca (Nice) http://math.unice.fr/~dimca/ Time: Tuesday, March 27, 12(NOON)--1PM Room: Carslaw 352 Lunch: after the talk --------------------------------------------------- Title: Chebyshev Curves and Hodge Theory Abstract: let $T_d(x)=\cos(d\arccos(x))$ be the classical Chebyshev polynomial of degree $d$. We consider the projective complex plane curve $C_d$ with affine equation $T_d(x)+T_d(y)=0$. We discuss the irreducible components of $C_d$ and the Hilbert-Poincare polynomial of the associated Jacobian ideal. Using Hodge theory in the form of Hodge-Deligne polynomials, we show that our results on the Chebyshev curves $C_d$ turn out to be quite general. --------------------------------------------------- Web site for Geometry Seminar is at: http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html