Abstract:
We describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding divisorial polytope. We compare our description with other possible descriptions of polarized complexity-one T-varieties. We also describe how to explicitly find generators of affine complexity-one T-varieties.
Reference:
Polarized complexity-1 T-varieties (Nathan Owen Ilten, Hendrik Süß), Michigan Mathematical Journal, volume 60, 2011.
Bibtex Entry:
@article{poltvars,
author="Ilten, Nathan Owen and S{\"u}{\ss}, Hendrik",
title={Polarized complexity-1 {T}-varieties},
journal = {Michigan Mathematical Journal},
volume = {60},
issue = {3},
pages = {561-578},
year = 2011,
url= {http://arxiv.org/abs/0910.5919},
gsid= {3321742852724470531},
doi= {10.1307/mmj/1320763049},
abstract={We describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding divisorial polytope. We compare our description with other possible descriptions of polarized complexity-one T-varieties. We also describe how to explicitly find generators of affine complexity-one T-varieties. },
}