• Corpus ID: 228063934

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… 

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