Work

Factorization centers in dimension 2 and the Grothendieck ring of varieties

Year: 2023

Type: article

Abstract: We initiate the study of factorization centers of birational maps and complete it for surfaces over a perfect field in this article.We prove that for every birational automorphism ϕ : X X of a smooth projective surface X over a perfect field k, the blowup centers are isomorphic to the blowdown centers in every weak factorization of ϕ.This implies that nontrivial L-equivalences of zero-dimensional varieties cannot be constructed based on birational automorphisms of a surface.It also implies that rationality centers are well defined for every rational surface X; namely, there exists a zero-dimensional variety intrinsic to X, which is blown up in any rationality construction of X.

Source: Algebraic geometry

DOI: 10.14231/ag-2023-024

Authors: Hsueh-Yung Lin, Evgeny Shinder, Susanna Zimmermann

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Center for Theoretical Sciences, Agence Nationale de la Recherche, Ministry of Education, Culture, Sports, Science and Technology, Conseil Régional des Pays de la Loire, National Science and Technology Council, Engineering and Physical Sciences Research Council

Awards: DERIVED CATEGORIES AND ALGEBRAIC K-THEORY OF SINGULARITIES, Fibrations and algebraic group actions, G4656594441

OpenAlex ID: W4388028126

FWCI: 2.064

Cites: 39

Cited by: 6

Related to: 10