# regular map

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## English[edit]

### Noun[edit]

**regular map** (*plural* **regular maps**)

- (algebraic geometry) A morphism between algebraic varieties.
**1994**, Miles Reid (translator), Igor R. Shafarevich,*Basic Algebraic Geometry 1*, 2nd Edition, Springer, page 29,- 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.

- We now find out how a
**2003**, Igor Dolgachev,*Lectures on Invariant Theory*, Cambridge University Press, page xiii,- Since one expects that the canonical projection is a
**regular map**of algebraic varieties and so has closed fibres, all orbits must be closed subsets in the Zariski topology of .

- Since one expects that the canonical projection is a
**2017**, José F. Fernando, José M. Gamboa, Carlos Ueno,*Polynomial, regular and Nash images of Euclidean spaces*, Fabrizio Broglia, Françoise Delon, Max Dickmann, Danielle Gondard-Cozette, Victoria Ann Powers (editors),*Ordered Algebraic Structures and Related Topics: International Conference*, American Mathematical Society, page 160,- The 1-dimensional semialgebraic set is the image of the
**regular map**- .

- The 1-dimensional semialgebraic set is the image of the

- (graph theory) 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.

- Just as there are only five
**2010**, Jozef Širáñ, Yan Wang,*Maps with highest level of symmetry that are even more symmetric than other such maps:*, Richard A. Brualdi, Samat Hedayat, Hadi Kharaghani, Gholamreza B. Khosrovshahi, Shahriar Shahriari (editors), (editors),**Regular maps**with largest exponent groups*Combinatorics and Graphs: The Twentieth Anniversary Conference of IPM Combinatorics*, American Mathematical Society, page 98,- 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.

- If
**2013**, Roman Nedela, Martin Škoviera,*7.6: Maps*, Jonathan L. Gross, Jay Yellen, Ping Zhang (editors),*Handbook of Graph Theory*, 2nd Edition, CRC Press, page 845,- If is a
**regular map**of type , then for some normal subgroup . Similar statements hold for the class of orientably**regular maps**and subgroups of and .

- If is a

#### Synonyms[edit]

- (function between algebraic varieties): morphism