arXiv subjects

Ludwig Balke

Publications and source records attributed to Ludwig Balke.

2 recordsLinked to original sources

arXiv1999

Smoothings of cyclic quotient singularities from a topological point of view

For a smoothing Y of a 2-dimensional cyclic quotient singularity X, we construct a simple handle decomposition of Y by using a particular birational map from Y to the projective plane. The manifold Y is built up from the product of an annulus with a disk by attaching 2-handles in a manner which can be described by means of a plumbing graph. In particular, Y is homotopy equivalent to a 2-dimensional CW-complex with 1-skeleton a single circle.

math.AG↗

arXiv1997

A note on P-resolutions of cyclic quotient singularities

P-resolutions of a cyclic quotient singularity are known to be in one-to-one correspondence with the components of the base space of its semi-universal deformation. Stevens and Christophersen have shown that P-resolutions are parametrized by so-called chains representing zero or, equivalently, certain subdivisions of polygons. I give here a purely combinatorial proof of the correspondence between subdivisions of polygons and P-resolutions.

alg-geom↗