## 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.
"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.