
	K3 surface constructions

This directory contains Mathematica programs to explicitly
construct K3 surfaces with given symmetries, via their
Hodge structures.  Output of these programs is also included,
as .txt files.

The general programs call "sage" and "gp" for certain number theory
functions.  These scripts have been tested with Mathematica 9.
f10.m constructs a K3 surface for the smallest Salem
number of degree 10, etc.  Much of the scripts will 
run without sage and gp.


EXAMPLE:
		cedar(424) math
		Mathematica 9.0 for Mac OS X x86 (64-bit)
		Copyright 1988-2013 Wolfram Research, Inc.

		In[1]:= <<f10.m

		[produces output describing K3 surface and its
		Hodge structure, including Pic, the Salem factor,
		the periodic factor, and the transcendental factor.
		This output is reproduced in f10.txt.]

Upon completion of execution, the variable "q"
contains a symmetric 22x22 matrix, representing the quadratic
form on H^2(X,Z), and the variable "f" contains a
22x22 matrix representing an automorphism of this
form with the desired characteristic polynomial.

In general information regarding the K3 surface can be
recovered from these 2 pieces of data by executing:

	DiK3[q,f].

=============================================================================
Copyright (c) Curtis T. McMullen, 2015
=============================================================================
