Examples violating Golyshev's canonical strip hypotheses
Algebraic Geometry
2022-06-09 v1
Abstract
We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomials of polarised varieties. They are given by moduli spaces of rank 2 bundles with fixed odd-degree determinant on curves of sufficiently high genus, hence our Fano examples have Picard rank 1, index 2, are rational, and have moduli. The hypotheses also fail for several other closely related varieties.
Keywords
Cite
@article{arxiv.1806.07648,
title = {Examples violating Golyshev's canonical strip hypotheses},
author = {Pieter Belmans and Sergey Galkin and Swarnava Mukhopadhyay},
journal= {arXiv preprint arXiv:1806.07648},
year = {2022}
}
Comments
8 pages, 1 table, 1 figure