Convex Geometry and Linear Series on Algebraic Varieties
卓士堯博士 下午 3:00–3:50 鴻經館 107 室 Bezout's theorem tells us that two polynomials f(x,y) and g(x,y) have (deg f)(deg g) common zeros in the projective plane. What about the number of common zeros in the affine plane? Interestingly, this number is related to the Newton polygons of f and g. We will begin with this first glimpse of connection between convex geometry and algebraic geometry, and proceed to introduce a recently developed generalization of this theory.