documentation:latest:fulton:versalcomponent

Available versions of this document: latest release, release 4.11, release 4.10, release 4.9, release 4.8, release 4.7, release 4.6, release 4.5, release 4.4, release 4.3, release 4.2, release 4.1, release 4.0, release 3.6, release 3.5, nightly master

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.

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


TOTAL_SPACE
Type:

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:
  :''[[..: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:

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: 2023/11/06 10:57
  • by 127.0.0.1