Work

Autoequivalences of blow‐ups of minimal surfaces

Year: 2024

Type: article

Abstract: Let be the blow‐up of in a finite set of very general points. We deduce from the work of Uehara [Trans. Amer. Math. Soc. 371 (2019), no. 5, 3529–3547] that has only standard autoequivalences, no non‐trivial Fourier–Mukai partners, and admits no spherical objects. If is the blow‐up of in 9 very general points, we provide an alternate and direct proof of the corresponding statement. Further, we show that the same result holds if is a blow‐up of finitely many points in a minimal surface of non‐negative Kodaira dimension which contains no ‐curves. Independently, we characterize spherical objects on blow‐ups of minimal surfaces of positive Kodaira dimension.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.13131

Authors: Xianyu Hu, Johannes Krah

Institutions: Technical University of Munich, Bielefeld University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funder: Deutsche Forschungsgemeinschaft