BigObject VersalComponent

from application fulton

A component of the versal deformation of a CyclicQuotient singularity.

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

TOTAL_SPACE

Type:

Ideal

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:
  :''[[..:common#Vector |Vector]]<[[..:common#Integer |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>