# Factorization centers in dimension two and the Grothendieck ring of varieties

@article{Lin2020FactorizationCI, title={Factorization centers in dimension two and the Grothendieck ring of varieties}, author={Hsueh-Yung Lin and Evgeny Shinder and Susanna Zimmermann}, journal={arXiv: Algebraic Geometry}, year={2020} }

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 $\phi : X \dashrightarrow X$ 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 $\phi$. This implies that nontrivial L-equivalences of $0$-dimensional varieties cannot be constructed based on birational automorphisms…

## 2 Citations

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. We construct invariants of birational maps with values in the Kontsevich–Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are…

### Burnside groups and orbifold invariants of birational maps

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. We construct new invariants of equivariant birational isomorphisms taking values in equivariant Burnside groups.

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