Enriques Surface

An Enriques surface X is a smooth compact complex surface having irregularity q(X)=0 and nontrivial canonical sheaf K_X such that K_X^2=O_X (Endraß). Such surfaces cannot be embedded in projective three-space, but there nonetheless exist transformations onto singular surfaces in projective three-space. There exists a family of such transformed surfaces of degree six which passes through each edge of a tetrahedron twice. A subfamily with tetrahedral symmetry is given by the two-parameter (r,c) family of surfaces


and the polynomial f_r is a sphere with radius r,



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Angermüller, G. and Barth, W. "Elliptic Fibres on Enriques Surfaces." Compos. Math. 47, 317-332, 1982.Barth, W. and Peters, C. "Automorphisms of Enriques Surfaces." Invent. Math. 73, 383-411, 1983.Barth, W. P.; Peters, C. A.; and van de Ven, A. A. Compact Complex Surfaces. New York: Springer-Verlag, 1984.Barth, W. "Lectures on K3- and Enriques Surfaces." In Algebraic Geometry, Sitges (Barcelona) 1983, Proceedings of a Conference Held in Sitges (Barcelona), Spain, October 5-12, 1983 (Ed. E. Casas-Alvero, G. E. Welters, and S. Xambó-Descamps). New York: Springer-Verlag, pp. 21-57, 1983.Endraß, S. "Enriques Surfaces.", F. Le superficie algebriche. Bologna, Italy: Zanichelli, 1949.Enriques, F. "Sulla classificazione." Atti Accad. Naz. Lincei 5, 1914.Hunt, B. The Geometry of Some Special Arithmetic Quotients. New York: Springer-Verlag, p. 317, 1996.Kim, Y. "Normal Quintic Enriques Surfaces." J. Korean Math. Soc. 36, 545-566, 1999.

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Enriques Surface

Cite this as:

Weisstein, Eric W. "Enriques Surface." From MathWorld--A Wolfram Web Resource.

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