Polynomial degree via pluripotential theory (Sione Ma'u, Auckland, Nouvelle Zélande)

08.10.2018 16:30

Given a complex polynomial pp in one variable, log|p|log⁡|p| is a subharmonic function that grows like (degp)log|z|(degp)log⁡|z| as |z|→∞|z|→∞. Such functions are studied using complex potential theory, based on the Laplace operator in the complex plane. Multivariable polynomials can also be studied using potential theory (more precisely, a non-linear version called pluripotential theory, which is based on the complex Monge-Ampere operator). In this talk I will motivate and define a notion of degree of a polynomial on an affine variety using pluripotential theory (Lelong degree). Using this notion, a straightforward calculation yields a version of Bezout's theorem. I will present some examples and describe how to compute Lelong degree explicitly on an algebraic curve. This is joint work with Jesse Hart.

Lieu

Bâtiment: Battelle

Séminaire "Fables géométriques "

Organisé par

Section de mathématiques

Intervenants

Sione Ma'u, Auckland, Nouvelle Zélande

entrée libre

Classement

Catégorie: Séminaire