Birational geometry via moduli spaces
Algebraic Geometry
2014-05-15 v1
Abstract
In this paper we connect degenerations of Fano threefolds by projections. Using Mirror Symmetry we transfer these connections to the side of Landau--Ginzburg models. Based on that we suggest a generalization of Kawamata's categorical approach to birational geometry enhancing it via geometry of moduli spaces of Landau--Ginzburg models. We suggest a conjectural application to Hasset--Kuznetsov--Tschinkel program based on new nonrationality "invariants" we consider --- gaps and phantom categories. We make several conjectures for these invariants in the case of surfaces of general type and quadric bundles.
Cite
@article{arxiv.1405.3374,
title = {Birational geometry via moduli spaces},
author = {Ivan Cheltsov and Ludmil Katzarkov and Victor Przyjalkowski},
journal= {arXiv preprint arXiv:1405.3374},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1405.2953