Martin's Blog

Polarisations on Hodge structures

Posted by Martin Orr on Saturday, 26 February 2011 at 18:27

In the last post, I discussed Hodge symplectic forms. Now I shall show that the H_1 of an abelian variety has a polarisation, which is defined to be a Hodge symplectic form satisfying a positivity condition. The importance of polarisations is that they give a way of recognising which H_1 Hodge structures come from abelian varieties - I shall discuss this application next time.

2 comments Tags abelian-varieties, alg-geom, hodge, maths