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arXiv · 1101.4884

4-dimensional symplectic contractions

Marco Andreatta·Jaroslaw A. Wisniewski
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Abstract

Local symplectic contractions are resolutions of singularities which admit symplectic forms. Four dimensional symplectic contractions are (relative) Mori Dream Spaces. In particular, any two such resolutions of a given singularity are connected by a sequence of Mukai flops. We discuss the cone of movable divisors on such a resolution; its faces are determined by curves whose loci are divisors, we call them essential curves. The movable cone is divided into nef chambers which are related to different resolutions; this subdivision is determined by classes of 1-cycles. We also study schemes parametrizing minimal essential curves and show that they are resolutions, possibly non-minimal, of surface Du Val singularities. Some examples, with an exhaustive description, are provided.

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Marco Andreatta, Jaroslaw A. Wisniewski. 2011-01-25. 4-dimensional symplectic contractions. https://doi.org/10.1007/s10711-013-9832-7

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