2010/09/25 by Hossein Movasati, Movasati, Hossein
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #math-ph #math.AG #math.CV #math.MP #math.NT
paper · pdf · doi:10.48550/arxiv.1009.5038
16 pages; Fields Communication Series, 2012
arxiv created 2012/04/10 · arxiv updated 2012/04/12
The space D of Hodge structures on a fixed polarized lattice is known as Griffiths period domain and its quotient by the isometry group of the lattice is the moduli of polarized Hodge structures of a fixed type. When D is a Hermition symmetric domain then we have automorphic forms on D, which according to Baily-Borel theorem, they give an algebraic structure to the mentioned moduli space. In this article we slightly modify this picture by considering the space U of polarized lattices in a fixed complex vector space with a fixed Hodge filtration and polarization. It turns out that the isometry group of the filtration and polarization, which is an algebraic group, acts on U and the quotient is again the moduli of polarized Hodge structures. This formulation leads us to the notion of quasi-automorphic forms which generalizes quasi-modular forms attached to elliptic curves.