On the Topology of Fano Smoothings

Tom Coates; Alessio Corti; Genival da Silva Jr

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arXiv · 1912.04383

On the Topology of Fano Smoothings

Tom Coates·Alessio Corti·Genival da Silva Jr

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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.

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Tom Coates, Alessio Corti, Genival da Silva Jr. 2019-12-09. On the Topology of Fano Smoothings. https://arxiv.org/abs/1912.04383

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