Communications in Number Theory and Physics

Volume 6 (2012)

Number 4

Some $tt$* structures and their integral Stokes data

Pages: 785 – 803



Martin A. Guest (Department of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo, Japan)

Chang-Shou Lin (Taida Institute for Mathematical Sciences, Center for Advanced Study in Theoretical Sciences, National Taiwan University, Taipei, Taiwan)


In Isomonodromy aspects of the $tt$* equations of Cecotti and Vafa I. Stokes data, by M.A. Guest, A.R. Its, and C.-S. Lin, a description was given of all smooth solutions of the two-function $tt$*-Toda equations in terms of asymptotic data, holomorphic data and monodromy data. In this supplementary paper, we focus on the holomorphic data and its interpretation in quantum cohomology, and enumerate those solutions with integral Stokes data. This leads to a characterization of quantum $D$-modules for certain complete intersections of Fano type in weighted projective spaces.

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