Examples Violating Golyshev's Canonical Strip Hypotheses. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Belmans, Pieter; Galkin, Sergey; Mukhopadhyay, Swarnava
• Is Part Of: Experimental mathematics. Volume 31:Issue 1(2022)
• Page Start: 233
• Page End: 237
• Publication Date: 2022-01-02
• Subjects: geography of Fano manifolds -- geography of Calabi-Yau manifolds -- roots of Hilbert polynomials -- Verlinde formula -- moduli spaces of vector bundles on algebraic curves; toric varieties; 14J45; 14J32; 14D20; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2019.1602571
• Languages: English
• ISSNs: 1058-6458

Abstract

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 polarized 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.