- Introduction
- Generalities
- General Surfaces
- Introduction
- Creation Functions
- Invariants
- GeometricGenus(S) : Srfc -> RngIntElt
- Plurigenus(S,n) : Srfc, RngIntElt -> 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 (H123E2)
- Singularity Properties
- Kodaira-Enriques Classification
- Minimal Models
- Special Surfaces in Projective 4-space
- Desingularisation by Blow Up
- Introduction
- Accessor Functions
- Multiplicities, Intersections and Restricted Linear Systems
- IntersectionMatrix(dsd) : DesingData -> Mtrx
- Multiplicities(S,D) : Srfc, DivSchElt -> SeqEnum
- MultiplicitiesAndIntersections(S,D) : Srfc, DivSchElt -> SeqEnum, SeqEnum
- IntersectionNumberOfStrictTransforms(S,D1,D2) : Srfc, Sch, Sch -> RngIntElt
- SelfIntersectionOfStrictTransform(S,D) : Srfc, Sch -> RngIntElt
- LinearSystemDivisorRestriction(S,B,ms) : Srfc, SeqEnum[RngMPolElt], SeqEnum[SeqEnum] -> SeqEnum
- Canonical Divisor Functionality
- Dual Resolution Graphs
- DualResolutionGraph(dsd) : DesingData -> GrphMultUnd, SeqEnum, SeqEnum
- MinimalDualResolutionGraph(dsd) : DesingData -> GrphMultUnd, SeqEnum, SeqEnum, Mtrx
- Example AlgSrf_srfc_dual_desing_grph_1 (H123E13)
- Example AlgSrf_srfc_dual_desing_grph_2 (H123E14)
- SelfIntersection(dsd,i) : DesingData,RngIntElt -> RngIntElt
- CanonicalIntersection(dsd,i) : DesingData,RngIntElt -> RngIntElt
- ArithmeticGenus(dsd,i) : DesingData,RngIntElt -> RngIntElt
- Genus(dsd,i) : DesingData,RngIntElt -> RngIntElt
- LocalIntersectionNumber(e) : GrphEdge -> RngIntElt
- Point counting on resolution fibres
- Extended Examples
- Surfaces in P3
- Del Pezzo Surfaces
- Introduction
- Creation of General Del Pezzos
- Some Auxiliary Intrinsics
- 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 (H123E29)
- 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 (H123E30)
- ParametrizeDegree5DelPezzo(X) : Sch -> MapIsoSch
- ParametrizeSingularDegree3DelPezzo(X,P2) : Sch, Prj -> BoolElt, MapIsoSch
- Example AlgSrf_del-pezzo-ex-3-sing (H123E31)
- 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 (H123E32)
- Cubic Surfaces over Finite Fields
- Construction of Cubic Surfaces
- Invariant Theory of Cubic Surfaces
- The Pentahedron of a Cubic Surface
- Degree 2 K3 Surfaces
- Introduction
- Creation Functions
- Split Divisors and Intersection Matrices
- Elliptic Fibrations
- KodairaConfigurations(imat) : Mtrx -> List
- Example AlgSrf_deg2K3_int_pairings (H123E42)
- EllipticFibrationRRSpaceDeg2K3(S,divlst,exdivlst) : Srfc, SeqEnum, SeqEnum -> SeqEnum[RngMPolElt],RngMPolElt
- EllipticGeneralFibreDeg2K3(S,B,secs) : Srfc, SeqEnum[RngMPolElt], SeqEnum[Sch] -> Crv,SeqEnum,SeqEnum
- Example AlgSrf_deg2K3-ell-fib-ex (H123E43)
- Bibliography
V2.28, 13 July 2023