  We consider the analytic properties of Feynman integrals from the perspective
of general A-discriminants and A-hypergeometric functions introduced by
Gelfand,Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and
mathematically rigour description of the singular locus, also known as Landau
variety, via principal A-determinants. We also comprise a description of the
various second type singularities. Moreover, by the
Horn-Kapranov-parametrization we give a very efficient way to calculate a
parametrization of Landau varieties. We furthermore present a new approach to
study the sheet structure of multivalued Feynman integrals by use of coamoebas.
