A tessellation for Fermat surfaces in CP3
| Autor: | Andrew J. Hanson, Ji-Ping Sha |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Surface (mathematics)
Fermat's Last Theorem Tessellation (computer graphics) Algebra and Number Theory Homogeneous coordinates Quadrilateral 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Pentahedron Combinatorics Computational Mathematics Face (geometry) Branched covering 0101 mathematics Mathematics |
| Zdroj: | Journal of Symbolic Computation. 44:591-605 |
| ISSN: | 0747-7171 |
| DOI: | 10.1016/j.jsc.2008.09.002 |
| Popis: | For each positive integer n, we present a tessellation of CP^2 that can be lifted, through the branched covering, to a symmetric tessellation of the Fermat surface (a 4-manifold) of degree n in CP^3. The process is systematic and symbolically algebraic. Each four-cell in the tessellation is bounded by four pentahedrons, and each pentahedron has four triangular faces and one quadrilateral face. Graphically, one can produce the entire surface from one single four-cell using translations generated by permutations and phase multiplications of the homogeneous coordinates of CP^3. Note that the tessellation of the Fermat surface of degree 4, a K3 surface, has exactly 24 vertices. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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