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On complex and symplectic toric stacks. (English) Zbl 1264.14002

Pragacz, Piotr (ed.), Contributions to algebraic geometry. Impanga lecture notes. Based on the Impanga conference on algebraic geometry, Banach Center, Bȩdlewo, Poland, July 4–10, 2010. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-114-9/hbk). EMS Series of Congress Reports, 305-331 (2012).
The authors show that the stacks resulting from the E. Lerman and S. Tolman construction [Trans. Am. Math. Soc. 349, No. 10, 4201–4230 (1997; Zbl 0897.58016)] construction (the refinement of T. Delzant construction [Bull. Soc. Math. Fr. 116, No. 3, 315–339 (1988; Zbl 0676.58029)] for rational but not necessarily smooth polytopes) are isomorphic to the stacks obtained by L. A. Borisov, L. Chen and G. G. Smith [J. Am. Math. Soc. 18, No. 1, 193–215 (2005; Zbl 1178.14057)] when the stacky fan is induced by a polytope. The authors also aim to give an example oriented introduction to symplectic toric geometry for a broader audience.
For the entire collection see [Zbl 1245.14003].

MSC:

14A20 Generalizations (algebraic spaces, stacks)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
53D05 Symplectic manifolds (general theory)
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