Formulas

Abstract

I want to recall some formulas which are used in the Maple/Sage scripts hodge.maple and hodge.sage avalable in http://www.math.purdue.edu/∼dvb/scripts/readme.html Given a smooth projective variety X, the ith Betti number bi(X) = dim H(X, Q) if it’s defined over C, and dim H(Xet, Q`) in general. The pqth Hodge number h(X) = dim H(X, ΩpX). These can be assembled into generating functions called the Poincaré and Hodge-Poincaré polynomials