Magma

MAGMA Computational Algebra System

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COHERENT SHEAVES

 
Acknowledgements
 
Introduction
 
Creation Functions
 
Accessor Functions
 
Basic Constructions
 
Sheaf Homomorphisms
 
Divisor Maps and Riemann-Roch spaces
 
Predicates
 
Miscellaneous
 
Examples
 
Bibliography







DETAILS

 
Introduction

 
Creation Functions
      Sheaf(M,X) : ModMPol, Sch -> ShfCoh
      StructureSheaf(X) : Sch -> ShfCoh
      CanonicalSheaf(X) : Sch -> ShfCoh
      Twist(S,n) : ShfCoh, RngIntElt -> ShfCoh

 
Accessor Functions
      Module(S) : ShfCoh -> ModMPol
      Scheme(S) : ShfCoh -> Sch
      FullModule(S) : ShfCoh -> ModMPol
      GlobalSectionSubmodule(S) : ShfCoh -> ModMPol
      SaturateSheaf(~S) : ShfCoh ->

 
Basic Constructions
      TensorProduct(S,T) : ShfCoh, ShfCoh -> ShfCoh
      Dual(S) : ShfCoh -> ShfCoh
      SheafHoms(S,T) : ShfCoh, ShfCoh -> ShfCoh, Map
      DirectSum(S,T) : ShfCoh, ShfCoh -> ShfCoh

 
Sheaf Homomorphisms
      SheafHomomorphism(S,T,h) : ShfCoh, ShfCoh, ModMPolHom -> ShfHom
      Domain(f) : ShfHom -> ShfCoh
      Codomain(f) : ShfHom -> ShfCoh
      Degree(f) : ShfHom -> RngIntElt
      ModuleHomomorphism(f) : ShfHom -> ModMPolHom
      Kernel(f) : ShfHom -> ShfCoh, ShfHom
      Image(f) : ShfHom -> ShfCoh, ShfHom, ShfHom
      Cokernel(f) : ShfHom -> ShfCoh, ShfHom
      Expand(hms) : SeqEnum[ShfHom] -> ShfHom

 
Divisor Maps and Riemann-Roch spaces
      DivisorMap(S) : ShfCoh -> Map,Sch
      DivisorToSheaf(X, I) : Sch, RngMPol -> ShfCoh
      Example Sheaf_shf:rr-scroll (H108E1)
      Example Sheaf_shf:dp3to6 (H108E2)

 
Predicates
      IsLocallyFree(S) : ShfCoh -> BoolElt, RngIntElt
      IsIsomorphic(S,T) : ShfCoh, ShfCoh -> BoolElt, ShfHom
      IsArithmeticallyCohenMacaulay(S) : ShfCoh -> BoolElt

 
Miscellaneous
      CohomologyDimension(S,r,n) : ShfCoh, RngIntElt, RngIntElt -> RngIntElt
      IntersectionPairing(S, T) : ShfCoh, ShfCoh -> RngIntElt

 
Examples
      Example Sheaf_big_ex (H108E3)

 
Bibliography

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