There is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35304 %1 35610 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-01-16T11:11:03Z No. of bitstreams: 1 Preprint_Davide.pdf: 1242726 bytes, checksum: 527d898383b9f997856370b14965bbdc (MD5) %0 Journal Article %J J.Phys.A: Math.Theor. 41,(2008), 205201-205247 %D 2008 %T On the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007) %A Davide Guzzetti %X We study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself. %B J.Phys.A: Math.Theor. 41,(2008), 205201-205247 %I SISSA %G en %U http://hdl.handle.net/1963/6521 %1 6473 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:36:09Z\nNo. of bitstreams: 1\n0801.1157v4.pdf: 449572 bytes, checksum: 6c4042b70a0d361af61282bee96d84db (MD5) %R 10.1088/1751-8113/41/20/205201