Smooth toric DM stacks

Abstract

We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.

37 pages, 4 figures, minor changes, to appear in Crelle

References in corpus (2)

• On the $K$-theory of smooth toric DM stacks
• Logarithmic geometry, minimal free resolutions and toric algebraic stacks

Cited by in corpus (6)

• Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
• Grothendieck Duality for Deligne-Mumford Stacks
• Equivariant Gromov-Witten theory of one dimensional stacks
• On Gromov-Witten theory of root gerbes
• A note on toric Deligne-Mumford stacks
• Mirror fibrations and root stacks of weighted projective spaces