Creation Functions
Surface(A,I) : Sch, ModMPol -> Srfc
Invariants
GeometricGenus(S) : Srfc -> RngIntElt
Plurigenus(S,n) : Srfc -> RngIntElt
ArithmeticGenus(S) : Srfc -> RngIntElt
Irregularity(S) : Srfc -> RngIntElt
ChernNumber(S,n) : Srfc, RngIntElt -> RngIntElt
MinimalChernNumber(S,n) : Srfc, RngIntElt -> RngIntElt
HodgeNumber(S,i,j) : Srfc, RngIntElt, RngIntElt -> RngIntElt
Example AlgSrf_srfcs-invs (H116E1)
Singularity Properties
IsNormal(S) : Srfc -> BoolElt
IsSimpleSurfaceSingularity(p) : Pt -> BoolElt, MonStr, RngIntElt
HasOnlySimpleSingularities(S) : Srfc -> BoolElt, List
Example AlgSrf_srfc_simp_sings (H116E2)
Kodaira-Enriques Classification
KodairaEnriquesType(S) : Srfc -> RngIntElt, RngIntElt, MonStr
KodairaEnriquesDimension(S) : Srfc -> RngIntElt
Example AlgSrf_srfc-kod-enr-ex (H116E3)
Minimal Models
MinimalModelRationalSurface(S) : Srfc -> Map
Example AlgSrf_min-mod-rat (H116E4)
MinimalModelRuledSurface(S) : Srfc -> Map
MinimalModelKodairaDimensionZero(S) : Srfc -> Map
Example AlgSrf_srfcs_kod_dim_0_min_mods1 (H116E5)
Example AlgSrf_srfcs_kod_dim_0_min_mods2 (H116E6)
MinimalModelKodairaDimensionOne(S) : Srfc -> Map, Map
MinimalModelGeneralType(S) : Srfc -> Map, BoolElt
CanonicalCoordinateIdeal(S) : Srfc -> RngMPol
Example AlgSrf_srfcs_gen_typ_min_mods1 (H116E7)
Example AlgSrf_srfcs_gen_typ_min_mods2 (H116E8)
Special Surfaces in Projective 4-space
RandomRationalSurface_d10g9(P) : Prj -> Srfc
RandomEnriquesSurface_d9g6(P) : Prj -> Srfc
RandomAbelianSurface_d10g6(P) : Prj -> Srfc
RandomEllipticFibration_d7g6(P) : Prj -> Srfc
RandomEllipticFibration_d8g7(P) : Prj -> Srfc
RandomEllipticFibration_d9g7(P) : Prj -> Srfc
RandomEllipticFibration_d10g10(P) : Prj -> Srfc
Embedded Formal Desingularization of Curves
ResolveAffineCurve(p) : RngMPolElt -> List, List, List, RngIntElt
Example AlgSrf_aff_crv_res (H116E9)
ResolveProjectiveCurve(p) : RngMPolElt -> List, List, List, RngIntElt
Example AlgSrf_prj_crv_res (H116E10)
Formal Desingularization of Surfaces
ResolveAffineMonicSurface(s) : RngUPolElt -> List, RngIntElt
Example AlgSrf_aff_res (H116E11)
ResolveProjectiveSurface(S) : Srfc -> List, RngIntElt
Example AlgSrf_prj_res (H116E12)
Adjoint Systems and Birational Invariants
HomAdjoints(m,n,S) : RngIntElt, RngIntElt, Srfc -> SeqEnum
GeometricGenusOfDesingularization(S) : Srfc -> RngIntElt
PlurigenusOfDesingularization(S,m) : Srfc, RngIntElt -> RngIntElt
ArithmeticGenusOfDesingularization(S) : Srfc -> RngIntElt
Example AlgSrf_adj_ex (H116E13)
Classification and Parameterization of Rational Surfaces
IsRational(X) : Srfc -> BoolElt
Reduction to Special Models
ClassifyRationalSurface(S) : Srfc -> Srfc, List, MonStgElt
Example AlgSrf_class (H116E14)
Parametrization of Rational Surfaces
ParametrizeProjectiveHypersurface(X, P2) : Srfc, Prj -> BoolElt, MapSch
ParametrizeProjectiveSurface(X, P2) : Srfc, Prj -> BoolElt, MapSch
Example AlgSrf_prm (H116E15)
Solve(p, F) : RngMPolElt, FldFunRat -> SeqEnum
Example AlgSrf_prm2 (H116E16)
Parametrization of Special Surfaces
ParametrizeQuadric(X,P2) : Sch, Prj -> BoolElt, MapSch
Example AlgSrf_solve_quad (H116E17)
ParametrizePencil(phi, P2) : MapSch, Prj -> BoolElt, MapSch
Example AlgSrf_ruled_ex (H116E18)
ParametrizeDelPezzo(X, P2) : Sch, Prj -> BoolElt, MapSch
Creation of General Del Pezzos
DelPezzoSurface(P,L) : Prj,List -> SrfDelPezzo
DelPezzoSurface(f) : RngMPolElt -> SrfDelPezzo
IsDelPezzo(Y) : Sch -> BoolElt, SrfDelPezzo, MapSch
Parametrization of Del Pezzo Surfaces
SetVerbose("ParamDP", v) : MonStgElt, RngIntElt ->
ParametrizeDegree9DelPezzo(X) : Sch -> BoolElt, MapIsoSch
ParametrizeDegree8DelPezzo(X) : Sch -> BoolElt, MapSch
Example AlgSrf_del-pezzo-ex-8 (H116E19)
ParametrizeDegree7DelPezzo(X) : Sch -> MapIsoSch
ParametrizeDegree6DelPezzo(X) : Sch -> BoolElt, MapIsoSch
Degree6DelPezzoType2_1(K,pt) : FldNum, Pt -> Sch
ParametrizeDelPezzoDeg6(X) : Sch -> BoolElt, MapIsoSch
Example AlgSrf_del-pezzo-ex-6 (H116E20)
ParametrizeDegree5DelPezzo(X) : Sch -> MapIsoSch
ParametrizeSingularDegree3DelPezzo(X,P2) : Sch, Prj -> BoolElt, MapIsoSch
Example AlgSrf_del-pezzo-ex-3-sing (H116E21)
Minimization and Reduction of Surfaces
MinimizeCubicSurface(f, p) : RngMPolElt, RngIntElt -> RngMPolElt, Mtrx
ReduceCubicSurface(f) : RngMPolElt -> RngMPolElt, Mtrx
MinimizeReduceCubicSurface(f) : MPolElt -> RngMPolElt, Mtrx
MinimizeDeg4delPezzo(f, p) : SeqEnum, RngIntElt -> SeqEnum, Mtrx
MinimizeReduceDeg4delPezzo(f) : SeqEnum -> SeqEnum, Mtrx
MinimizeReduce(S) : SrfDelPezzo -> SrfDelPezzo, Mtrx
Example AlgSrf_dp34 (H116E22)
Cubic Surfaces over Finite Fields
NumberOfPointsOnCubicSurface(f) : RngMPolElt -> RngIntElt, RngIntElt
Example AlgSrf_numptscubic (H116E23)
IsIsomorphicCubicSurface(f,g) : MPolElt, MPolElt -> BoolElt, List
Example AlgSrf_isisocubic (H116E24)
Construction of Cubic Surfaces
CubicSurfaceByHexahedralCoefficients(p) : RngUPolElt -> RngMPolElt
CoblesRadicand(p) : RngUPolElt -> FldElt
Example AlgSrf_hex (H116E25)
Invariant Theory of Cubic Surfaces
Invariants
ClebschSalmonInvariants(f) : RngMPolElt -> SeqEnum, RngElt
SkewInvariant100(f) : RngMPolElt -> RngElt
CubicSurfaceFromClebschSalmon(inv) : SeqEnum -> RngMPolElt
Example AlgSrf_inv_cub (H116E26)
Covariants
LinearCovariants(f) : RngMPolElt -> SeqEnum
ClassicalCovariantsOfCubicSurface(f) : RngMPolElt -> SeqEnum
Contravariants
NumericClebschTransfer(f, inv, p) : RngMPolElt, UserProgram, SeqEnum -> RngElt
ContravariantsOfCubicSurface(f) : RngMPolElt -> SeqEnum
Example AlgSrf_cayley_dual (H116E27)
Interaction of Covariants and Contravariants
ApplyContravariant(c, d) : MPolElt, MPolElt -> MPolElt
Example AlgSrf_co_cont (H116E28)
The Pentahedron of a Cubic Surface
PentahedronIdeal(f) : RngMPolElt -> RngMPol
Example AlgSrf_penta (H116E29)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012