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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

# BigObject VersalComponent

from application fulton

A component of the versal deformation of a CyclicQuotient singularity.

### Algebraic Geometry

Properties relevant for the algebro-geometric side of the components of the versal deformation of CQS.

TOTAL_SPACE
Type:
Ideal

### Combinatorics

These properties capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

ALPHA_LATTICE

Lattice of alphas as in below article.

Jan Arthur Christophersen: On the components and discriminant of the versal base space of cyclic quotient singularities.
Type:
Map<Vector<Integer>,Vector<Integer>>

CONTINUED_FRACTION

The continued fraction equivalent to zero describing the versal component. See

Jan Arthur Christophersen: On the components and discriminant of the versal base space of cyclic quotient singularities.

and

Jan Stevens: On the versal deformation of cyclic quotient singularities.
Type:
Vector<Integer>

CQS_MATRIX

The CQS matrix as described in Def 6.10 of the below article.

Theo de Jong, Duco van Straten: Deformation theory of sandwiched singularities.
Type:
Matrix<Rational,NonSymmetric>

DIMENSION

Dimension of this component, i.e., number of parameters.

Type:
Integer

N_GON_TRIANGULATION

Triangulation of the N-gon corresponding to this component. See

Jan Stevens: On the versal deformation of cyclic quotient singularities.
Type:
Graph<Undirected>

PYRAMID_LATTICE

Type:
Map<Vector<Integer>,Vector<Integer>>

P_RESOLUTION

The P-resolution fan corresponding to this component. See

Klaus Altmann: P-Resolutions of Cyclic Quotients from the Toric Viewpoint.
Type:
PolyhedralFan<Rational>

TRIANGLES

The triangles in the N-gon triangulation corresponding to this component. See

Jan Stevens: On the versal deformation of cyclic quotient singularities.
Type:
Matrix<Integer,NonSymmetric>

• documentation/latest/fulton/versalcomponent.txt