search for "{* temporarily disabled" to find the 1 disabled bits of example code
The other six were for hilbertPolynomial, which is okay.

Cc: Michael Stillman <mike@math.cornell.edu>
From: David Eisenbud <de@msri.org>
To: dan@math.uiuc.edu
In-Reply-To: <200812102118.mBALI3do020929@u123.math.uiuc.edu>
Subject: Re: hilbertFunction
Date: Wed, 10 Dec 2008 13:45:30 -0800

Dear Dan and Mike,

Certainly I would not have expected that for a coherent sheaf!

There I would expect the Hilbert function of the global section module.
If the given underlying module M has depth >= 2, this is the same,
but not otherwise. The right function H(m) can be computed
for n > n_0, say, tas the Hilbert function of

Hom(mm^d, M),

where mm is the maximal homogeneous ideal and d is computed from
the Castelnuovo-Mumford regularity of M (as a module over a polynomial
ring.)

This is all a little complicated. Worth including "automatically"?

Regards,

David


--
David Eisenbud
Professor of Mathematics,
University of California, Berkeley
www.msri.org/~de


On Dec 10, 2008, at 1:18 PM, Daniel R. Grayson wrote:

>
> For a projective variety hilbertFunction() simply applies itself to  
> the
> underlying graded ring.  Similarly for coherent sheaves.  This might  
> be
> unexpected behavior.  Should we fix it?


