Ample tangent bundle on smooth projective stacks

2016/11/06 by Haloui, Karim El
#14A20 #18E40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.01809

Abstract

We study ample vector bundles on smooth projective stacks. In particular, we prove that the tangent bundle for the weighted projective stack ℙ(a₀,...,a_n) is ample. A result of Mori shows that the only smooth projective varieties with ample vector bundle are isomorphic to ℙ^N for some N. Extending our geometric spaces from varieties to projective stacks, we are able to provide a new example. This leaves the open question of knowing if the only smooth projective stacks are the weighted projective stacks.

Related

• Toric varieties with ample tangent bundle
• Characterization theorems for the projective space and vector bundle adjunction
• Caractérisations des espaces projectifs et des quadriques
• Embeddings of weighted projective spaces
• Ample vector bundles and moduli of tame stacks