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GROWI - Andreas Gathmann

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Andreas Gathmann - GROWI

GROWI is a C++ program for the computation of Gromov-Witten invariants. The current version 1.0.3 can compute:

  • (absolute) Gromov-Witten invariants of projective spaces in any genus,
  • (absolute) Gromov-Witten invariants of any hypersurface in a projective space in genus 0,
  • relative Gromov-Witten invariants of projective spaces relative any hypersurface in genus 0.
"Descendants" can be used in all these invariants.

Examples

Computation of a single Gromov-Witten invariant:

  > growi lines in cubic surface 
27
> growi elliptic cubics in P^2 thru H^2:9
1
> growi G=2,D=5 in P^4 thru H^3*psi^22
-41369/110075314176

Writing a C++ program that uses the GROWI functions: with the following file test.cm

  // Elliptic space curves of degree d through 2d points 

int main (int argc, char *argv[])
{
    rational n0,n1;

    for (int d=1; d<=8; d++) {
        n0 = GW (rational D=d in P^3 thru H^3:2*d);
        n1 = GW (elliptic D=d in P^3 thru H^3:2*d);
        cout << d << ": " << n1+(2*d-1)/12*n0 << endl;
    }
}

one gets

  > growi test.cm 
1: 0
2: 0
3: 0
4: 1
5: 42
6: 2860
7: 225734
8: 23276160

System Requirements

GROWI should run on any UNIX system with C++ compiler, the GNU MP library, and the GNU DBM library.

Remarks

The calculation of invariants in high degree and/or genus might need very large amounts of memory and/or computation time.

For the computations GROWI uses the methods of:

  • A. Gathmann, Absolute and relative Gromov-Witten invariants of very ample hypersurfaces, Duke Mathematical Journal 115 (2002) no. 2, 171-203 (pdf)
  • A. Gathmann, Topological recursion relations and Gromov-Witten invariants in higher genus, e-print math.AG/0305361 (pdf)

Installation instructions can be found in the README file in the distribution packet.

Download

growi-1.0.3.tar.gz