4-dimensional symplectic contractions

Details 4-dimensional symplectic contractions 4-dimensional symplectic contractions

2011-01-25

arxiv.org/abs/1101.4884v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

Four dimensional symplectic resolutions are (relative) Mori Dream Spaces. Any two such resolutions are connected by a sequence of Mukai flops. We discuss cones of their movable divisors with faces determined by curves whose loci are divisors, we call them essential curves. These cones are divided into nef chambers related to different resolutions, the division is determined by classes of flopping 1-cycles. We also study schemes parametrizing minimal essential curves and show that they are resolutions, possibly non-minimal, of surface Du Val singularities.

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