Varieties : Table of Contents

• Varieties -- affine and projective algebraic geometry

  • Variety -- the class of all algebraic varieties
  • AffineVariety -- the class of all affine varieties
  • ProjectiveVariety -- the class of all projective varieties
  • CoherentSheaf -- the class of all coherent sheaves
  • SheafOfRings -- the class of sheaves of rings
  • SumOfTwists -- the class of all sums of twists
  • SheafMap (missing documentation)
• > ZZ
• >= ZZ
• AffineVariety ** Ring
• annihilator(CoherentSheaf) -- the annihilator ideal
• canonicalBundle (missing documentation)
• char(AffineVariety) -- the characteristic of the coordinate ring of a variety
• codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety
• codim(Variety) -- codimension of a variety
• coherent sheaves
• CoherentSheaf (*) -- sum of twists
• CoherentSheaf ** CoherentSheaf -- tensor produce of coherent sheaves
• CoherentSheaf ++ CoherentSheaf -- direct sum of coherent sheaves
• CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves
• CoherentSheaf ^ ZZ -- direct sum
• CoherentSheaf ^** ZZ -- tensor power
• CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• cotangentSheaf -- cotangent sheaf of a projective variety
• cotangentSheaf(ProjectiveVariety) -- cotangent sheaf of a projective variety
• cotangentSheaf(ZZ,ProjectiveVariety) -- exterior powers of the cotangent sheaf of a projective variety
• degree(ProjectiveVariety)
• dim(AffineVariety) -- dimension of the affine variety
• dim(ProjectiveVariety) -- dimension of the projective variety
• dual(CoherentSheaf) -- dual coherent sheaf
• euler -- Euler characteristic
• euler(CoherentSheaf) -- Euler characteristic of coherent sheaf
• euler(Ideal)
• euler(Module)
• euler(ProjectiveHilbertPolynomial) -- constant term of the Hilbert polynomial
• euler(ProjectiveVariety) -- topological Euler characteristic of a (smooth) projective variety
• euler(Ring)
• eulers -- list the sectional Euler characteristics
• eulers(CoherentSheaf)
• eulers(Ideal)
• eulers(Ring)
• Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
• exteriorPower(ZZ,CoherentSheaf)
• genera -- list of the successive linear sectional arithmetic genera
• genera(CoherentSheaf)
• genera(Ideal)
• genera(ProjectiveVariety)
• genera(Ring)
• genus -- arithmetic genus
• genus(CoherentSheaf)
• genus(ProjectiveVariety)
• genus(Ring)
• GlobalSectionLimit (missing documentation)
• hh -- Hodge numbers of a smooth projective variety
• HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety
• HH^ZZ SumOfTwists -- coherent sheaf cohomology module
• HH^ZZ(ProjectiveVariety,CoherentSheaf) -- cohomology of a coherent sheaf on a projective variety
• hilbertPolynomial(CoherentSheaf) -- compute the Hilbert polynomial of the coherent sheaf
• hilbertPolynomial(ProjectiveVariety) -- compute the Hilbert polynomial of the projective variety
• Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• ideal(Variety) -- returns the defining ideal
• isLiftable (missing documentation)
• isProjective (missing documentation)
• LowerBound -- the class of lower bound objects
• module(CoherentSheaf) -- get the module defining a coherent sheaf
• module(SheafOfRings)
• numgens(CoherentSheaf) -- the number of generators of the underlying module
• OO -- the structure sheaf
• pdim(CoherentSheaf) -- calculate the projective dimension
• Proj -- make a projective variety
• ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• ring(Variety) -- coordinate ring of the variety
• SaturationMap (missing documentation)
• sheaf -- make a coherent sheaf
• sheaf(Module) -- make a coherent sheaf
• sheaf(Ring) -- make a coherent sheaf of rings
• sheaf(Variety) -- make a coherent sheaf
• sheaf(Variety,Module) -- make a coherent sheaf
• sheaf(Variety,Ring) -- make a coherent sheaf of rings
• SheafExpression -- the class of sheaf expressions
• sheafExt -- sheaf Ext of coherent sheaves
• sheafHom -- sheaf Hom
• sheafMap (missing documentation)
• SheafOfRings ^ List -- make a graded free coherent sheaf
• Spec -- make an affine variety
• tangentSheaf -- tangent sheaf of a projective variety
• tangentSheaf(ProjectiveVariety) -- tangent sheaf of a projective variety
• TorsionFree (missing documentation)
• variety -- get the variety
• variety(CoherentSheaf) -- get the variety
• variety(Ideal) -- the closed projective subvariety defined by an ideal
• variety(Ring) -- the variety previously associated to a given ring
• variety(SheafOfRings) -- get the variety