| Title | Inverse Problem and Monodromy Data for Three-Dimensional Frobenius Manifolds |
| Publication Type | Journal Article |
| Year of Publication | 2001 |
| Authors | Guzzetti, D |
| Journal | Mathematical Physics, Analysis and Geometry 4: 245–291, 2001 |
| Keywords | Frobenius Manifolds, Painleve Equations, Isomonodromy deformations |
| Abstract | We study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we\r\nexplicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlevé VI\r\ntranscendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric\r\nform to explicitly construct polynomial and algebraic solutions and to derive the generating\r\nfunction of Gromov–Witten invariants of the quantum cohomology of the two-dimensional projective\r\nspace. The procedure is a relevant application of the theory of isomonodromic deformations. |
| DOI | 10.1023/A:1012933622521 |
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