Project Points

 

Leader of the project

 

 

 

Ferruccio Orecchia

orecchia@unina.it

  

Participants in the working group

 

 

 

Ferruccio Orecchia

orecchia@unina.it

 

 

 

Francesca Cioffi

cioffifr@unina.it

 

 

 

Isabella Ramella

ramella@matna2.dma.unina.it

  

Collaborators

 

 

 

Giovanna Albano

albano@diima.unisa.it

 

 

 

Luca Chiantini

chiantini@unisi.it

 

 

 

Alessandro De Paris

deparis@unina.it

 

 

Description

Project Points intends to construct algorithms and to implement sofwares concerning problems in Algebraic Geometry which need the computation of the Hilbert Function or of minimal generators or of the resolution of the ideal of a finite set of points (the points can be also fat).

 

Software

Points, release 3.7, is an experimental version of a software package containing the implementation of the algorithms related to the Project Points. Hence, it offers the computation of the Hilbert function and of minimal generators of the ideals of a finite set of points or of rational varieties over finite fields of type Z_p or over the field Q of rational numbers. We are still working to improve it.

All the algorithms implemented in Points have polynomial computational cost.
The features are:

  -1- Computations on zero-dimensional schemes:
          simple points:
             -1- Hilbert function of ideals of projective points.
             -2- Minimal generators of ideals of projective points.
             -3- Conductor of projective points.
             -4- Checking the Ideal Generation Conjecture (only on Z_p).
          fat points:
             -1- Hilbert function of ideals of fat projective points.
             -2- Hilbert function of ideals of the projective closure of affine fat
                  points.
             -3- Minimal generators of ideals of fat projective points.
             -4- Maximal rank and minimally generation of ideals of fat points.
  -2- Minimal generators of ideals of parametric rational curves.
  -3- Minimal generators of ideals of parametric varieties up to a given degree.
  -4- Hilbert function and minimal generators of ideals of elliptic curves
       computed as birational images of plane elliptic curves (only on Z_p).
In some particular cases it is also possible to compute minimal generators of the first linear syzygies.

Points is available in compiled version for PC Pentium (running Linux 2.4.3):

and for Mac Os X:

To unpack the softwares do:   tar –xvzf  xxx.tgz.

We are looking forward to receiving useful feedbacks. For any comments and bug reports, please contact one of the participants in the working group. 

(Last update: 08 - 03 - 2010)