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This is a list of named (classes of) algebraic surfaces and complex surfaces. The notation κ stands for the Kodaira dimension, which divides surfaces into four coarse classes. ==Algebraic and complex surfaces== * abelian surfaces (κ = 0) Two-dimensional abelian varieties. * algebraic surfaces * Barlow surfaces General type, simply connected. * Barth surfaces Surfaces of degrees 6 and 10 with many nodes. * Beauville surfaces General type * bielliptic surfaces (κ = 0) Same as hyperelliptic surfaces. * Bordiga surfaces A degree-6 embedding of the projective plane into P4 defined by the quartics through 10 points in general position. * Burniat surfaces General type * Campedelli surfaces General type * Castelnuovo surfaces General type * Catanese surfaces General type * Cayley nodal cubic surface Rational. A cubic surface with 4 nodes. * Cayley's ruled cubic surface * Châtelet surfaces Rational * class VII surfaces κ = −∞, non-algebraic. * Clebsch surface Rational. The surface Σ''x''''i'' = Σ''x''''i''3 = 0 in P4. * Coble surfaces Rational * cubic surfaces Rational. * Del Pezzo surfaces Rational. Anticanonical divisor is ample, for example P2 blown up in at most 8 points. * Dolgachev surfaces Elliptic. * elliptic surfaces Surfaces with an elliptic fibration. * Endrass surface A surface of degree 8 with 168 nodes * Enneper surface * Enoki surface Class VII * Enriques surfaces (κ = 0) * exceptional surfaces: Picard number has the maximal possible value ''h''1,1. * fake projective plane general type, found by Mumford, same Betti numbers as projective plane. * Fano surface of lines on a non-singular 3-fold. It can also mean del Pezzo surface. * Fermat surface of degree ''d'': Solutions of ''w''''d'' + ''x''''d'' + ''y''''d'' + ''z''''d'' = 0 in P3. * general type κ = 2 * generalized Raynaud surface in positive characteristic * Godeaux surfaces (general type) * Hilbert modular surfaces * Hirzebruch surfaces Rational ruled surfaces. * Hopf surfaces κ = −∞, non-algebraic, class VII * Horikawa surfaces general type * Horrocks–Mumford surfaces. These are certain abelian surfaces of degree 10 in P4, given as zero sets of sections of the rank 2 Horrocks–Mumford bundle. * Humbert surfaces These are certain surfaces in quotients of the Siegel upper half-space of genus 2. * hyperelliptic surfaces κ = 0, same as bielliptic surfaces. * Inoue surfaces κ = −∞, class VII,''b''2 = 0. (Several quite different families were also found by Inoue, and are also sometimes called Inoue surfaces.) * Inoue-Hirzebruch surfaces κ = −∞, non-algebraic, type VII, ''b''2>0. * K3 surfaces κ = 0, supersingular K3 surface. * Kähler surfaces complex surfaces with a Kähler metric, which exists if and only if the first Betti number ''b''1 is even. * Kato surface Class VII * Klein icosahedral surface The Clebsch cubic surface or its blowup in 10 points. * Kodaira surfaces κ = 0, non-algebraic * Kummer surfaces κ = 0, special sorts of K3 surfaces. * Labs surface A surface of degree 7 with 99 nodes * minimal surfaces Surfaces with no rational −1 curves. (They have no connection with minimal surfaces in differential geometry.) * Mumford surface A "fake projective plane" * non-classical Enriques surface Only in characteristic 2. * numerical Campedelli surfaces surfaces of general type with the same Hodge numbers as a Campedelli surface. * numerical Godeaux surfaces surfaces of general type with the same Hodge numbers as a Godeaux surface. * Picard modular surface * Plücker surface Birational to Kummer surface * projective plane Rational * properly elliptic surfaces κ = 1, elliptic surfaces of genus ≥2. * quadric surfaces Rational, isomorphic to P1 × P1. * quartic surfaces Nonsingular ones are K3s. * quasi Enriques surface These only exist in characteristic 2. * quasi elliptic surface Only in characteristic ''p'' > 0. * quasi-hyperelliptic surface * quotient surfaces: Quotients of surfaces by finite groups. Examples: Kummer, Godeaux, Hopf, Inoue surfaces. * rational surfaces κ = −∞, birational to projective plane * Raynaud surface in positive characteristic * Reye congruence A special sort of Enriques surface. κ=0. * Roman surface * ruled surfaces κ = −∞ * Sarti surface A degree-12 surface in P3 with 600 nodes. * Segre surface An intersection of two quadrics, isomorphic to the projective plane blown up in 5 points. * Steiner surface A surface in P4 with singularities which is birational to the projective plane. * surface of general type κ = 2. * Tetrahedroid A special Kummer surface. * Togliatti surfaces, degree-5 surfaces in P3 with 31 nodes. * unirational surfaces Castelnuovo proved these are all rational in characteristic 0. * Veronese surface An embedding of the projective plane into P5. * Wave surface A special Kummer surface. * Weddle surface κ = 0, birational to Kummer surface. * White surface Rational. * Zariski surfaces (only in characteristic ''p'' > 0): There is a purely inseparable dominant rational map of degree ''p'' from the projective plane to the surface. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of complex and algebraic surfaces」の詳細全文を読む スポンサード リンク
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