2014/01/22 by Murad Alim, Alim, Murad · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG
paper · pdf · doi:10.48550/arxiv.1401.5537
10 pages, 2 figures, contribution to the proceedings of the String-Math 2013 conference
arxiv created 2014/01/22 · arxiv updated 2014/01/23
An overview is given of the construction of a differential polynomial ring of functions on the moduli space of Calabi-Yau threefolds. These rings coincide with the rings of quasi modular forms for geometries with duality groups for which these are known. They provide a generalization thereof otherwise. Higher genus topological string amplitudes can be expressed in terms of the generators of this ring giving them a global description in the moduli space. An action of a duality exchanging large volume and conifold loci in moduli space is discussed. The connection to quasi modular forms is illustrated by the local P2 geometry and its mirror, the generalization is extended to several compact geometries with one-dimensional moduli spaces.