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Cayley's cubic surface is the unique cubic surface having four ordinary double points (Hunt), the maximum possible for cubic surface (Endraß). The Cayley cubic is invariant ...

Let f be a bounded analytic function on D(0,1) vanishing to order m>=0 at 0 and let {a_j} be its other zeros, listed with multiplicities. Then ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...

In the plane, there are 17 lattice groups, eight of which are pure translation. In R^3, there are 32 point groups and 230 space groups. In R^4, there are 4783 space lattice ...

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...

A topological space is locally connected at the point x if every neighborhood of x contains a connected open neighborhood. It is called locally connected if it is locally ...

The holomorphic tangent bundle to a complex manifold is given by its complexified tangent vectors which are of type (1,0). In a coordinate chart z=(z_1,...,z_n), the bundle ...

A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...