Combinatorial properties of the K3 surface: Simplicial blowups and slicings

Details Combinatorial properties of the K3 surface: Simplicial blowups and slicings Combinatorial properties of the K3 surface: Simplicial blowups and slicings

2009-09-08

arxiv.org/abs/0909.1453v2

Spreer, Jonathan; K\"uhnel, Wolfgang Combinatorial properties of the K3 surface: simplicial blowups and slicings. Exp. Math. 2

Mathematics

Combinatorics

31 pages, 3 figures

Scientific paper

The 4-dimensional abstract Kummer variety K^4 with 16 nodes leads to the K3 surface by resolving the 16 singularities. Here we present a simplicial realization of this minimal resolution. Starting with a minimal 16-vertex triangulation of K^4 we resolve its 16 isolated singularities - step by step - by simplicial blowups. As a result we obtain a 17-vertex triangulation of the standard PL K3 surface. A key step is the construction of a triangulated version of the mapping cylinder of the Hopf map from the real projective 3-space onto the 2-sphere with the minimum number of vertices. Moreover we study simplicial Morse functions and the changes of their levels between the critical points. In this way we obtain slicings through the K3 surface of various topological types.

Affiliated with

Also associated with

No associations

Rating

Combinatorial properties of the K3 surface: Simplicial blowups and slicings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Combinatorial properties of the K3 surface: Simplicial blowups and slicings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Combinatorial properties of the K3 surface: Simplicial blowups and slicings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108198