Birational types of algebraic orbifolds

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Аннотация

We introduce a variant of the birational symbols group of Kontsevich, Pestun and the second author, and use this to define birational invariants of algebraic orbifolds. Bibliography: 20 titles.

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Авторлар туралы

Andrew Kresch

Institut für Mathematik, Universität Zürich

PhD, Professor

Yuri Tschinkel

Courant Institute of Mathematical Sciences; Simons Foundation

Email: tschinkel@cims.nyu.edu

Әдебиет тізімі

  1. D. Abramovich, T. Graber, A. Vistoli, “Gromov–Witten theory of Deligne–Mumford stacks”, Amer. J. Math., 130:5 (2008), 1337–1398
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  3. D. Abramovich, M. Temkin, “Functorial factorization of birational maps for qe schemes in characteristic $0$”, Algebra Number Theory, 13:2 (2019), 379–424
  4. K. Behrend, B. Noohi, “Uniformization of Deligne–Mumford curves”, J. Reine Angew. Math., 2006:599 (2006), 111–153
  5. D. Bergh, “Functorial destackification of tame stacks with abelian stabilisers”, Compos. Math., 153:6 (2017), 1257–1315
  6. D. Bergh, D. Rydh, Functorial destackification and weak factorization of orbifolds
  7. E. Bierstone, P. D. Milman, “Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant”, Invent. Math., 128:2 (1997), 207–302
  8. F. Bittner, “The universal Euler characteristic for varieties of characteristic zero”, Compos. Math., 140:4 (2004), 1011–1032
  9. К. С. Браун, Когомологии групп, Наука, М., 1987, 384 с.
  10. C. Cadman, “Using stacks to impose tangency conditions on curves”, Amer. J. Math., 129:2 (2007), 405–427
  11. S. Keel, S. Mori, “Quotients by groupoids”, Ann. of Math. (2), 145:1 (1997), 193–213
  12. S. L. Kleiman, A. B. Altman, “Bertini theorems for hypersurface sections containing a subscheme”, Comm. Algebra, 7:8 (1979), 775–790
  13. M. Kontsevich, V. Pestun, Yu. Tschinkel, “Equivariant birational geometry and modular symbols”, J. Eur. Math. Soc. (to appear)
  14. M. Kontsevich, Yu. Tschinkel, “Specialization of birational types”, Invent. Math., 217:2 (2019), 415–432
  15. A. Kresch, “On the geometry of Deligne–Mumford stacks”, Algebraic geometry, Part 1 (Seattle, 2005), Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009, 259–271
  16. A. Kresch, “Destackification with restricted root operations”, Eur. J. Math., 4:4 (2018), 1421–1432
  17. Ю. И. Манин, “Параболические точки и дзета-функции модулярных кривых”, Изв. АН СССР. Сер. матем., 36:1 (1972), 19–66
  18. I. Moerdijk, “Orbifolds as groupoids: an introduction”, Orbifolds in mathematics and physics (Madison, WI, 2001), Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002, 205–222
  19. J. Oesinghaus, “Conic bundles and iterated root stacks”, Eur. J. Math., 5:2 (2019), 518–527
  20. O. E. Villamayor, “Patching local uniformizations”, Ann. Sci. Ecole Norm. Sup. (4), 25:6 (1992), 629–677

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© Креш Э., Чинкель Ю., 2021

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