This is the directory: genus2, which contains files
relating to curves of genus 2.
The following gives the subdirectories, and the files they contain.
DIRECTORY: durham
Contains the jpg files of the transparencies for the talk
I gave at the LMS Durham Symposium, August 2000.
For Professor Cremona's homepage of the Symposium,
including the online proceedings, see:
http://www.maths.nottingham.ac.uk/personal/jec/durham/index.html
DIRECTORY: bruinflynn
Contains files relating to computations in the two
joint articles: "N-Covers of Hyperelliptic Curves"
and "Elementary 2-covers of hyperelliptic curves"
by N. Bruin and E.V. Flynn.
DIRECTORY: jacobian.variety
Contains the files:
bilinear.forms
Gives the forms phi_{ij}(a,b), each bilinear in the jacobian
variety coordinates of a and b, such that projectively
k_i(a-b) * k_j(a+b).
defining.equations
Gives a set of defining equations for the jacobian variety.
DIRECTORY kummer.
Contains the files:
biquadratic.forms
Gives the 4 x 4 array BBB of quadratic forms on the kummer surface
such that, projectively:
( BBB[i,j] ) = ( k_i(A+B) k_j(A-b) + k_i(A-B) k_j(A+B) )
defining.equations
Gives the defining equation for the kummer surface, and
a formula for addition by a point of order 2.
duplication
Gives the formula for the duplication law on the kummer surface.
DIRECTORY local
Contains the files:
formal.group
Gives terms of the formal group up to and including degree 7.
local.coordinates
Gives the first few terms for the expansions for the local
coordinates as power series in the local parameters s1,s2.
exp
Gives the formal exponential power series up to and including degree 7.
log
Gives the formal logarithmic power series up to and including degree 7.
DIRECTORY maple
Contains the files:
Appl.pro
An application.
This program makes use of the formulae and procedures constructed
in the programs Kummer to check the results of Section 6
of Chapter 3, "The Kummer surface", in the book
"Progelomana to a middlebrow arithmetic of curves of genus 2".
by J.W.S. Cassels and E.V. Flynn (Cambridge University Press, 1996)
group.law
Performs the group law on divisors.
kernel.of.mu
Gives an easy way to check whether Criterion (ii) of Lemma 6.5.1
(in the same book as above) is satisfied.
Kummer.pro
Gives a program which makes use of the formulae and procedures constructed
in the programs Kummer to check the results of Section 6
of Chapter 3, "The Kummer surface", in the same book as above.
DIRECTORY misc
Contains the file:
people
Gives the e-mail addresses of people who
have either recently published work in genus 2, or are currently
working on problems in genus 2.
DIRECTORY out.of.date
This directory contains some old files from the days
when I was using a slightly different embedding of
the jacobian variety. I suggest that you don't bother
with these files.
DIRECTORY qderived
Contains the file:
appendix.ps
This is an appendix (in postscript) to the article:
"On Q-Derived Polynomials", to appear in
Proc. Edinburgh Math. Soc. It only makes sense
if read in conjunction with that article!
DIRECTORY rank.tables
Contains the file:
ranks1
This currently contains only those ranks for which
descriptions of the computations have been published.
I shall at some stage include other ranks which have
been computed, once I have decided on a good reader-verification
format. That is to say, a concise piece of information
which the reader can use to check the correctness
of the rank computation.
DIRECTORY typos
Contains the file:
first.edition.first.printing
This gives typo corrections for the first edition, first
printing of "Prolegomena to a Middlebrow Arithmetic of
Curves of Genus 2", by J.W.S. Cassels and E.V. Flynn (CUP, 1996).