- Introduction
- Hilbert Series and Graded Rings
- Baskets of Singularities
- Generic Polarised Varieties
- Subcanonical Curves
- Creation of Subcanonical Curves
- SubcanonicalCurve(g,d,Q) : RngIntElt,RngIntElt,SeqEnum -> GRCrvK
- IsSubcanonicalCurve(g,d,Q) : RngIntElt,RngIntElt,SeqEnum -> BoolElt,GRCrvK
- HilbertPolynomialOfCurve(g,m) : RngIntElt,RngIntElt -> RngUPolElt
- IsEffective(C) : GRCrvK -> BoolElt
- Catalogue of Subcanonical Curves
- K3 Surfaces
- Weil Polynomials
- SetVerbose("WeilPolynomials", v) : MonStgElt, RngIntElt ->
- HasAllRootsOnUnitCircle(f) : RngUPolElt -> BoolElt
- FrobeniusTracesToWeilPolynomials(tr, q, i, deg) : SeqEnum, RngIntElt, RngIntElt, RngIntElt -> SeqEnum
- WeilPolynomialToRankBound(f, q) : RngUPolElt, RngIntElt -> RngIntElt
- ArtinTateFormula(f, q, h20) : RngUPolElt, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- WeilPolynomialOverFieldExtension(f, deg) : RngUPolElt, RngIntElt -> RngUPolElt
- CheckWeilPolynomial(f, q, h20) : RngUPolElt, RngIntElt, RngIntElt -> BoolElt
- Example GrdRng_weilpoly (H125E5)
- Example GrdRng_weilpoly2 (H125E6)
- Point Counting on Degree Two K3 Surfaces
- The K3 Database
- Searching the K3 Database
- Working with the K3 Database
- K3Surface(D,i) : DB,RngIntElt -> GRK3
- K3Surface(D,Q,i) : DB,SeqEnum,RngIntElt -> GRK3
- K3Surface(D,g,i) : DB,RngIntElt,RngIntElt -> GRK3
- K3Surface(D,g1,g2,i) : DB,RngIntElt,RngIntElt,RngIntElt -> GRK3
- K3Surface(D,W) : DB,SeqEnum -> GRK3
- K3Surface(D,g,B) : DB,RngIntElt,GRBskt -> GRK3
- Fano 3-folds
- Example GrdRng_gr-fano (H125E10)
- Creation: f=1, 2 or ≥3
- A Preliminary Fano Database
- FanoDatabase() : -> DB
- Fano(D,i) : DB,RngIntElt -> GRFano
- Fano(D,f,i) : DB,RngIntElt,RngIntElt -> GRFano
- Fano(D,f,Q,i) : DB,SeqEnum,RngIntElt -> GRFano
- Calabi--Yau 3-folds
- CalabiYau(p1,p2,B) : RngIntElt,RngIntElt,GRBskt -> GRCY
- FindN(X) : GRCY -> RngIntElt,RngIntElt
- FindN(p1,p2,B) : RngIntElt,RngIntElt,GRBskt -> RngIntElt,RngIntElt
- Building Databases
- Bibliography
V2.28, 13 July 2023