We show that for an irreducible subvariety Y of an abelian variety X the
Gauss mapping, from the conormal bundle of $Y$ to the dual of the tangent space
of $X$ at the origin, is not dominant if and only if Y is degenerate in the
sense that there exists a nontrivial abelian subvariety A of X such that A+Y=Y
holds
We prove multiplicity one for vector valued holomorphic Siegel modular forms
of weights greater or equal to 3 and the full Siegel modular group and give a
trace formula for the action of the Hecke operators T(p) in the regular cases.
We prove multiplicity one for vector valued holomorphic Siegel modular forms
of weights greater or equal to 3 and the full Siegel modular group and give a
trace formula for the action of the Hecke operators T(p) in the regular cases.
A semisimple algebraic tensor category over an algebraically closed field k
of characteristic zero is the representation category of all finite dimensional
twisted super representations of an affine reductive supergroup G over k. Such
a supergroup is reductive if and only if its connected component is reductive.
The connected component is reductive if and only if the Lie superalgebra
divided by its center is a product of simple Lie algebras of classical type and
Lie superalgebras spo(1,2r) of the orthosymplectic types BC_r.
A semisimple algebraic tensor category over an algebraically closed field k
of characteristic zero is the representation category of all finite dimensional
twisted super representations of an affine reductive supergroup G over k. Such
a supergroup is reductive if and only if its connected component is reductive.
The connected component is reductive if and only if the Lie superalgebra
divided by its center is a product of simple Lie algebras of classical type and
Lie superalgebras spo(1,2r) of the orthosymplectic types BC_r.