Fibred toric varieties in toric hyperkähler varieties

Details Fibred toric varieties in toric hyperkähler varieties Fibred toric varieties in toric hyperkähler varieties

2010-12-11

arxiv.org/abs/1012.2427v3

Mathematics

Algebraic Geometry

21 pages, 5 figures, 3rd version, the whole paper is revised

Scientific paper

We introduce the fibred toric varieties as equivariant $\mathbb{C}P^r$ bundles over lower dimensional toric varieties. An equivalent characterization is that the natural morphisms on them degenerate to bundle projections in the context of variation of toric varieties as GIT quotients. Our main observation is that these fibred toric varieties also arise naturally in the variation of hyperk\"{a}hler varieties, namely, the fibred toric varieties are contained in the exceptional sets of the hyperk\"{a}hler natural morphisms and the Mukai flops.

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