On the Topology of Fano Smoothings
Algebraic Geometry
2019-12-11 v1
Abstract
Suppose that X is a Fano manifold that corresponds under Mirror Symmetry to a Laurent polynomial f, and that P is the Newton polytope of f. In this setting it is expected that there is a family of algebraic varieties over the unit disc with general fiber X and special fiber the toric variety defined by the spanning fan of P. Building on recent work and conjectures by Corti--Hacking--Petracci, who construct such families of varieties, we determine the topology of the general fiber from combinatorial data on P. This provides evidence for the Corti--Hacking--Petracci conjectures, and verifies that their construction is compatible with expectations from Mirror Symmetry.
Cite
@article{arxiv.1912.04383,
title = {On the Topology of Fano Smoothings},
author = {Tom Coates and Alessio Corti and Genival da Silva},
journal= {arXiv preprint arXiv:1912.04383},
year = {2019}
}
Comments
16 pages, 16 figures