GROWI - A program for the computation of Gromov-Witten invariants
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.
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.