Simple elliptic singularities: a note on their G-function

Strachan, I. A.B. (2012) Simple elliptic singularities: a note on their G-function. Asian Journal of Mathematics, 16(3), pp. 409-426. (doi: 10.4310/AJM.2012.v16.n3.a3)

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The link between Frobenius manifolds and singularity theory is well known, with the simplest examples coming from the simple hypersurface singularities. Associated with any such manifold is a function known as the G-function. This plays a role in the construction of higher-genus terms in various theories. For the simple singularities the G-function is known explicitly: G = 0. The next class of singularities, the unimodal hypersurface or elliptic hypersurface singularities consists of three examples, Ẽ6, Ẽ7, Ẽ8 (or equivalently P8,X9, J10). Using a result of Noumi and Yamada on the flat structure on the space of versal deformations of these singularities the G-function is explicitly constructed for these three examples. The main property is that the function depends on only one variable, the marginal (dimensionless) deformation variable. Other examples are given based on the foldings of known Frobenius manifolds. Properties of the G-function under the action of the modular group is studied, and applications within the theory of integrable systems are discussed.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Strachan, Professor Ian
Authors: Strachan, I. A.B.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Asian Journal of Mathematics
Publisher:International Press
ISSN (Online):1945-0036
Published Online:27 September 2012
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