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 ${\mathbb{CP}}^3$ of degree $d\ge 5$ can be decomposed as the union of $d(d-4{)}^2$ copies of 4-dimensional pair-of-pants and certain subsets of K3 surfaces.

arXiv comment42

References in corpus (5)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• KAWA lecture notes on the Kähler-Ricci flow
• A survey of Einstein metrics on 4-manifolds
• Riemannian geometry of Kahler-Einstein currents III: compactness of Kahler-Einstein manifolds of negative scalar curvature
• Degeneration of Kahler-Einstein hypersurfaces in complex torus to generalized pair of pants decomposition