Characterization of affine varieties being cones over nonsingular projective manifolds and sharp estimate of integral points in real tetrahedron
 

Stephen S.T. YAU
UI Chicago, USA
 
 
 

Abstract

In this talk we shall discuss the problem of characterization of affine varieties being cones over nonsingular projective manifolds. We shall also discuss how the problem is related to the sharp estimate of integral points in real n-dimensional tetrahedron. Asymptotic estimates of integral points in real n-dimensional tetrahedron were obtained by Hardy-Littlewood and Spencer. We shall report the current progress in the Granville-Lin-Yau conjecture on sharp polynomial estimate.