Pair-of-Pants Decompositions of 4-Manifolds Diffeomorphic to General Type Hypersurfaces

Abstract

In this paper, we show that a smooth 4-manifold diffeomorphic to a complex hypersurface in $\mathbb{C} \mathbb{P}^{3}$ of degree d≥5 can be decomposed as the union of d(d−4)² copies of 4-dimensional pair-of-pants and certain subsets of K3 surfaces.

Keywords

Pair-of-pants decompositions / general type hypersurfaces