Wolfram Decker 1/5/1993

This folder contains programs which compute the equations and syzygies
of all smooth nongeneral type surfaces in P4 known to us. For smoothness 
and adjunction see the folders with the scripts.

How to construct the surfaces is described in in the main part
and in Appendix B of our paper

     Decker, Ein, Schreyer: ... Journal of Algebraic Geometry 1993.

and in

     Popescu: Thesis, Saarbruecken, 1993.

We will update our programs in case new surfaces will be constructed.
Wright now ( 1/5/1993 ) there are 3 surfaces not mentioned in Appendix B 
above:
- Nonminimal abelian surfaces with degree d=15, and sectional genus g=21
  lying on one quintic hypersurface only ( compare the above thesis ).
- Nonminimal bielliptic surfaces with degree d=15, and sectional genus g=21
- Enriques surfaces with d=13 and g=16.
The latter surface is not mentioned in Appendix B above, since we did not
prove yet that this surface and the one  described in our paper are in
different components of the Hilbert scheme ( though this is quite likely ).

How to construct the abelian and bielliptic surfaces will be described
in the forthcoming paper 
     
    Aure, Decker, Hulek, Popescu, Ranestad: Syzygies of abelian and
                                               bielliptic surfaces in P4.

The programs follow precisely the description in our paper ( for some 
surfaces we provide alternative constructions too ). Especially
we explicitely compute the mapping cone of phi e Hom(F,G) which is costly
concerning time and memory. Many of the set degree commands should be
considered just as comments. They are not necessary for the actual 
computation. To save time and memory some easy changes can be made:
- Choose random matrices more sparse and/or eg. modulo 7 ( and verify
  by your computation that your choices are general enough ).
- Avoid computations of dual modules if not actually needed.
- Do not compute mapping cones directly. Use appropriate syzygy
  computations instead.

We use the following scripts of David Eisenbud.

% <stack

;;; Usage:
;;;      <stack newmat mat1 .. matn
;;;
;;;    Creates a matrix newmat with rows the rows of mat1 ... matn 
;;; in order.

% <ideal

;;; Usage:
;;;     <ideal j f1 f2 ... fn
;;;
;;; Creates an ideal j over the current ring with generators f1, ..., fn.

% <random_mat

;;; Usage:
;;;     <random_mat a b i m
;;;
;;; defines an  a x b  matrix m whose entries are random linear
;;; combinations of the entries of the 1xn matrix i.  The rowdegs of m
;;; are all = 0.

If these are not available on your machine replace them appropriately.

For questions please contact me, Wolfram Decker, at
    decker@math.uni-sb.de.
For questions concerning the thesis of Sorin Popescu contact
    popescu@math.uni-sb.de.
Comments, suggestions and new surfaces are welcome.
