regular map

Noun

regular map (plural regular maps)

1. A morphism between algebraic varieties.
   • We now find out how a regular map acts on the ring of regular functions on a closed set.[…]Moreover, regular maps can be characterised as the maps that take regular functions into regular functions.1994, Igor R. Shafarevich, translated by Miles Reid, Basic Algebraic Geometry 1, 2nd edition, Springer, page 29
   • Since one expects that the canonical projection f#58;X#92;rightarrowX#47;G is a regular map of algebraic varieties and so has closed fibres, all orbits must be closed subsets in the Zariski topology of X.2003, Igor Dolgachev, Lectures on Invariant Theory, Cambridge University Press, page xiii

   Synonyms:

   morphism

2. A symmetric tessellation of a closed surface; a decomposition of a two-dimensional manifold into topological disks such that every flag (incident vertex-edge-face triple) can be transformed into any other flag by a symmetry (i.e., an automorphism) of the decomposition.
   • 1990 [McGraw-Hill], Jay Kappraff, Connections: The Geometric Bridge Between Art and Science, 2001, World Scientific, page 141,
     Just as there are only five regular maps on the sphere (or plane), there are only three classes of regular maps that can be created on a torus.
   • If n is finite, the regular map is a tessellation of the plane by congruent n-sided polygons, m of which meet at each vertex.2010, Jozef Širáñ, Yan Wang, “Maps with highest level of symmetry that are even more symmetric than other such maps: Regular maps with largest exponent groups”, in Richard A. Brualdi, Samat Hedayat...