Symplectic rational blow-ups on rational 4-manifolds

Heesang Park; Dongsoo Shin

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arXiv · 2111.07501

Symplectic rational blow-ups on rational 4-manifolds

Heesang Park·Dongsoo Shin

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Abstract

We prove that if a symplectic 4-manifold $X$ becomes a rational 4-manifold after applying rational blow-down surgery, then the symplectic 4-manifold $X$ is originally rational. That is, a symplectic rational blow-up of a rational symplectic $4$-manifold is again rational. As an application we show that a degeneration of a family of smooth rational complex surfaces is a rational surface if the degeneration has at most quotient surface singularities, which generalizes slightly a classical result of [B\u{a}descu, 1986] in algebraic geometry under a mild additional condition.

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BibTeX RIS

Heesang Park, Dongsoo Shin. 2021-11-15. Symplectic rational blow-ups on rational 4-manifolds. https://arxiv.org/abs/2111.07501

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