Geometric interpretation of Hermitian modular forms via Burkhardt invariants

Abstract

We give a complete theta expression of a pair of Hermitian modular forms as an inverse period mapping of lattice polarized $K3$ surfaces. Our result gives a non-trivial relation among moduli of $K3$ surfaces, theta functions and the finite complex reflection group of rank $5$.

arXiv comment18 pages, 4 figures, 7 Tables ; Minor changes (minor typos are corrected)

References in corpus (2)

• A theta expression of the Hilbert modular functions for $\sqrt{5}$ via the periods of $K3$ surfaces
• Inverse period mappings of $K3$ surfaces and a construction of modular forms for a lattice with the Kneser conditions

Cited by in corpus (1)

• Sequence of families of lattice polarized $K3$ surfaces, modular forms and degrees of complex reflection groups