1. Symplectic rational blow-ups on rational 4-manifolds.
- Author
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Park, Heesang and Shin, Dongsoo
- Subjects
ALGEBRAIC geometry ,MATHEMATICS - 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 Bădescu [J. Reine Angew. Math. 367 (1986), pp. 76–89] in algebraic geometry under a mild additional condition. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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