This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== BigObject CyclicQuotient ====== //from application [[..:fulton|fulton]]//\\ \\ An affine normal toric variety given by a two-dimensional cone in two-dimensional space. ? derived from: : ''[[..:fulton:NormalToricVariety |NormalToricVariety]]'' ===== Properties ===== ==== Algebraic Geometry ==== Properties relevant for the algebro-geometric side of CQS. ---- {{anchor:versal_component:}} ? **''VERSAL_COMPONENT''** :: The components of the versal deformation. ? Type: :''[[..:fulton:VersalComponent |VersalComponent]]'' ---- {{anchor:versal_components:}} ? **''VERSAL_COMPONENTS''** :: The continued fractions equivalent to zero that index the components of the versal deformation. See > Jan Arthur Christophersen: On the components and discriminant of the versal base space of cyclic quotient singularities. ? Type: :''[[..:common#Matrix |Matrix]]<[[..:common#Rational |Rational]],[[..:common#NonSymmetric |NonSymmetric]]>'' ---- ==== Input properties ==== Properties defining a cyclic quotient singularity. Please be careful in checking the consistency if you give multiple input properties. ---- {{anchor:continued_fraction:}} ? **''CONTINUED_FRACTION''** :: Representation of the number n/q as a Hirzebruch-Jung continued fraction. Take care that this property agrees with the dual property. ? Type: :''[[..:common#Vector |Vector]]<[[..:common#Integer |Integer]]>'' ---- {{anchor:dual_continued_fraction:}} ? **''DUAL_CONTINUED_FRACTION''** :: Representation of the number n/(n-q) as a Hirzebruch-Jung continued fraction. Take care that this property agrees with the dual property. ? Type: :''[[..:common#Vector |Vector]]<[[..:common#Integer |Integer]]>'' ---- {{anchor:n:}} ? **''N''** :: Every cyclic quotient variety corresponds to a cone given by the rays (1,0) and (-q,n). ? Type: :''[[..:common#Integer |Integer]]'' ---- {{anchor:q:}} ? **''Q''** :: Every cyclic quotient variety corresponds to a cone given by the rays (1,0) and (-q,n). ? Type: :''[[..:common#Integer |Integer]]'' ---- documentation/release/3.6/fulton/cyclicquotient.txt Last modified: 2019/11/15 22:01by 127.0.0.1