SMS scnews item created by Zhou Zhang at Thu 22 Mar 2012 1100
Type: Seminar
Distribution: World
Expiry: 12 Apr 2012
Calendar1: 27 Mar 2012 1200-1300
CalLoc1: Carslaw 352

Geometry Seminar: Dimca -- Chebyshev Curves and Hodge Theory

Speaker: Prof. Alexandru Dimca (Nice)

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.


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