Humbert surface
Encyclopedia
In algebraic geometry
, a Humbert surface, studied by , is a surface
in the moduli space
of principally polarized abelian surface
s consisting of the surfaces with a symmetric endomorphism of some fixed discriminant
.
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, a Humbert surface, studied by , is a surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
in the moduli space
Moduli space
In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects...
of principally polarized abelian surface
Abelian surface
In mathematics, an abelian surface is 2-dimensional abelian variety.One dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic...
s consisting of the surfaces with a symmetric endomorphism of some fixed discriminant
Discriminant
In algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial's roots. For example, the discriminant of the quadratic polynomialax^2+bx+c\,is\Delta = \,b^2-4ac....
.