## Chebyshev curves and Hodge theory

Alex Dimca
Nice University, France.

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-Poincar\'e 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.