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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:

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:

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:

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:

DIMENSION

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

Type:

N_GON_TRIANGULATION

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

Jan Stevens: On the versal deformation of cyclic quotient singularities.
Type:

PYRAMID_LATTICE

FIXME

Type:

P_RESOLUTION

The P-resolution fan corresponding to this component. See

Klaus Altmann: P-Resolutions of Cyclic Quotients from the Toric Viewpoint.
Type:

TRIANGLES

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

Jan Stevens: On the versal deformation of cyclic quotient singularities.
Type:

  • documentation/latest/fulton/versalcomponent.txt
  • Last modified: 2019/08/13 10:31
  • (external edit)