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THE K3 DATABASE

 
Introduction
      Geometry and Basic Conventions
      An Example of Use of the Database
 
Accessing the K3 Database
      The Database Itself
      Searching the Database
      K3 Surfaces in the Database
 
Relations between K3 Surfaces
      Projection and Unprojection
 
Building the K3 Database
      Gathering the Data
      Working with the Raw Elements
 
Bibliography







DETAILS

 
Introduction

      Geometry and Basic Conventions
            Degree(g,B) : RngIntElt,SeqEnum -> FldRatElt
            HilbertSeries(g,B) : RngIntElt,SeqEnum -> FldFunRatUElt
            HilbertSeries(F,V) : SeqEnum,SeqEnum -> FldFunRatUElt

      An Example of Use of the Database

 
Accessing the K3 Database

      The Database Itself
            K3Database() : -> SeqEnum
            SetAFR(~DB) : SeqEnum ->

      Searching the Database
            K3SurfacesFromWeights(DB,W) : SeqEnum,SeqEnum -> SeqEnum
            K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
            K3SurfaceFromAFR(DB,c,n) : SeqEnum,RngIntElt,RngIntElt -> VSrfK3
            K3Surface(DB,i) : SeqEnum,RngIntElt -> VSrfK3
            X eq Y : VSrfK3,VSrfK3 -> BoolElt

      K3 Surfaces in the Database
            Number(X) : VSrfK3 -> RngIntElt
            Weights(X) : VSrfK3 -> SeqEnum
            Basket(X) : VSrfK3 -> SeqEnum
            Indices(X) : VSrfK3 -> SeqEnum
            Codimension(X) : VSrfK3 -> RngIntElt
            Genus(X) : VSrfK3 -> RngIntElt
            HilbertNumerator(X) : VSrfK3 -> RngUPolElt
            HilbertSeries(X,W) : VSrfK3,SeqEnum -> FldFunRatUElt
            Degree(X) : VSrfK3 -> FldRatElt
            HilbertSeries(X) : VSrfK3 -> FldFunRatUElt
            HilbertCoefficients(X,n) : VSrfK3,RngIntElt -> SeqEnum
            AFRNumber(X) : VSrfK3 -> RngIntElt
            HilbertForm(X) : VSrfK3 -> SeqEnum

 
Relations between K3 Surfaces

      Projection and Unprojection
            Centres(~X,DB) : VSrfK3,SeqEnum ->
            Centres(X) : VSrfK3 -> SeqEnum
            HasCentreType(X,i) : VSrfK3,RngIntElt -> BoolElt
            Example K3_k3-projection (H91E1)
            ProjectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
            Unprojections(~X,DB) : VSrfK3,SeqEnum ->
            Unprojections(X) : VSrfK3 -> SeqEnum
            Example K3_k3-unprojection (H91E2)
            UnprojectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
            Example K3_k3-unprojection-chain (H91E3)

 
Building the K3 Database

      Gathering the Data
            Baskets(n) : RngIntElt -> SeqEnum,SeqEnum,SeqEnum,SeqEnum
            Example K3_k3-baskets (H91E4)

      Working with the Raw Elements
            K3Surface(g,B) : RngIntElt,SeqEnum -> VSrfK3
            AddWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
            AddLocalGenerators(X) : VSrfK3 -> VSrfK3
            ApparentCodimension(X) : VSrfK3 -> RngIntElt

 
Bibliography