Wing Keung To, National U. Singapore

Effective Lojasiewicz inequality and stability of bihomogeneous polynomials

In this talk I will describe some joint work with Sai-Kee Yeung on getting two effective versions of effective Lojasiewicz inequality for affine algebraic varieties defined by homogeneous polynomials over a number filed.  This work is motivated from our earlier study of certain stability property of bihomogeneous polynomials which are positive on C^n,  or more generally, those which are positive on affine algebraic varieties.  In addition, I will also discuss the semi-stability problem for non-negative bihomogeneous polynomials and some preliminary related result in a pet project with my MSc student Ms Hoi-Nam Mok.