TY - JOUR
T1 - Inverse Problem and Monodromy Data for Three-Dimensional Frobenius Manifolds
JF - Mathematical Physics, Analysis and Geometry 4: 245–291, 2001
Y1 - 2001
A1 - Davide Guzzetti
KW - Frobenius Manifolds, Painleve Equations, Isomonodromy deformations
AB - 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.
PB - RIMS, Kyoto University
U1 - 6479
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -