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.

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References in corpus (3)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• A survey of Einstein metrics on 4-manifolds
• Degeneration of Kahler-Einstein hypersurfaces in complex torus to generalized pair of pants decomposition