Revisiting toric SU(3) structures

Understand

Three-dimensional smooth compact toric varieties (SCTV) admit SU(3) structures, and may thus be relevant for string compactifications, if they have even first Chern class (c1).

• This condition can be fulfilled by infinitely many SCTVs, including CP3 and CP1 bundles over all two-dimensional SCTVs.
• We show that as long as c1 is even, toric SU(3) structures can be constructed using a method proposed in arXiv:1005.2194.
• We perform a systematic study of the parametric freedom of the resulting SU(3) structures, with a particular focus on the metric and the torsion classes.