Algebraic surface with special triviality properties
In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0.
Over fields of characteristic not 2 they are quotients of K3 surfaces by a group of order 2 acting without fixed points and their theory is similar to that of algebraic K3 surfaces. Enriques surfaces were first studied in detail by Enriques (1896) as an answer to a question discussed by Castelnuovo (1895) about whether a surface with q = pg = 0 is necessarily rational, though some of the Reye congruences introduced earlier by Reye (1882) are also examples of Enriques surfaces.
Enriques surfaces can also be defined over other fields.
Over fields of characteristic other than 2, Artin (1960) showed that the theory is similar to that over the complex numbers. Over fields of characteristic 2 the definition is modified, and there are two new families, called singular and supersingular Enriques surfaces, described by Bombieri & Mumford (1976). These two extra families are related to the two non-discrete algebraic group schemes of order 2 in characteristic 2.
In mathematics, Enriquessurfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial...
younger brother was zoologist Paolo Enriques who was also the father of Enzo Enriques Agnoletti and Anna Maria Enriques Agnoletti. He became a student of...
named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification...
of the 10 or so classes of surface in the Enriques–Kodaira classification of complex surfaces, and were the first surfaces to be investigated. Every non-singular...
K3 surface. Certain K3 surfaces in non-zero characteristic. Supersingular Enriquessurface. Certain Enriquessurfaces in characteristic 2. A surface is...
the theorem of Babbage-Chisini-Enriques (for Dennis Babbage who completed the proof, Oscar Chisini and Federigo Enriques). The terminology is confused...
an elliptic surface (with no singular fibers). All surfaces of Kodaira dimension 1 are elliptic surfaces. Every complex Enriquessurface is elliptic,...
finite abelian group. Hyperelliptic surfaces form one of the classes of surfaces of Kodaira dimension 0 in the Enriques–Kodaira classification. The Kodaira...
0 to vanish while h0,1 is positive, while Mumford showed that for Enriquessurfaces in characteristic 2 it is possible for h0,1 to vanish while h1,0 is...
curves of genus g ≥ 2 has dimension 3g − 3. The Enriques–Kodaira classification classifies algebraic surfaces: coarsely by Kodaira dimension, then in more...
form on a smooth projective surface that is not closed, and shows that Hodge symmetry fails for classical Enriquessurfaces in characteristic two. This...
(elliptic curve); and g > 1 (Riemann surfaces with independent holomorphic differentials). In the case of surfaces, the Enriques classification was into five...
Kodaira surfaces have the same relation to primary ones that Enriquessurfaces have to K3 surfaces, or bielliptic surfaces have to abelian surfaces. Invariants:...
under the supervision of Oscar Zariski, defending a thesis about Enriquessurfaces. In the early 1960s, Artin spent time at the IHÉS in France, contributing...
Levi. His wife Elbina Marianna Enriques was the sister of mathematician Federigo Enriques and zoologist Paolo Enriques. After attending a grammar school...
Chapter 2. Eisenhart 2004, p. 110. Stillwell 1996; Bonola, Carslaw & Enriques 1955. Wilson 2008, Chapter 5. Taylor 1996b, p. 107; Berger 1977, pp. 341–343...
a fibration. Ruled surfaces appear in the Enriques classification of projective complex surfaces, because every algebraic surface of Kodaira dimension...
example. It also applies to some other varieties, such as Enriquessurfaces and some surfaces of general type. A source of examples is Orlov's blowup formula...
In April 2019, an Israeli lunar lander, Beresheet, crash landed on the surface of the Moon carrying a copy of nearly all of the English Wikipedia engraved...
shows all automorphism groups of singular cubic surfaces with no parameters. Algebraic surfaceEnriques–Kodaira classification Fano variety Schubert calculus...
manifolds. He introduced Reye congruences, the earliest examples of Enriquessurfaces. Scott, Charlotte Angas (1899). "Reye's Geometrie der Lage". Bull...
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