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Abstract

The codimension of the complement of the set of factorial hypersurfaces of degree d in PN is estimated for d ≥ 4 and N ≥ 7.

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References

  1. F. Call and G. Lyubeznik, “A simple proof of Grothendieck’s theorem on the parafactoriality of local rings,” in Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra (Am. Math. Soc., Providence, RI, 1994), Contemp. Math. 159, pp. 15–18.

    Google Scholar 

  2. I. A. Cheltsov, “Factoriality of nodal three-dimensional varieties and connectedness of the locus of log canonical singularities,” Mat. Sb. 197 (3), 87–116 (2006) [Sb. Math. 197, 387–414 (2006)].

    Article  MathSciNet  MATH  Google Scholar 

  3. I. Cheltsov, “Factorial threefold hypersurfaces,” J. Algebr. Geom. 19 (4), 781–791 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  4. I. Cheltsov and J. Park, “Factorial hypersurfaces in P4 with nodes,” Geom. Dedicata 121, 205–219 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  5. C. Ciliberto and V. Di Gennaro, “Factoriality of certain threefolds complete intersection in P5 with ordinary double points,” Commun. Algebra 32 (7), 2705–2710 (2004).

    Article  MATH  Google Scholar 

  6. M. Mella, “Birational geometry of quartic 3-folds. II: The importance of being Q-factorial,” Math. Ann. 330 (1), 107–126 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Polizzi, A. Rapagnetta, and P. Sabatino, “On factoriality of threefolds with isolated singularities,” Mich. Math. J. 63 (4), 781–801 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces,” Invent. Math. 134 (2), 401–426 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. V. Pukhlikov, “Birationally rigid Fano complete intersections,” J. Reine Angew. Math. 541, 55–79 (2001).

    MathSciNet  MATH  Google Scholar 

  10. A. Pukhlikov, Birationally Rigid Varieties (Am. Math. Soc., Providence, RI, 2013), Math. Surv. Monogr. 190.

    Book  MATH  Google Scholar 

  11. A. V. Pukhlikov, “Birational geometry of Fano hypersurfaces of index two,” Math. Ann. 366 (1–2), 721–782 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces,” Izv. Ross. Akad. Nauk, Ser. Mat. 81 (3), 160–188 (2017) [Izv. Math. 81, 618–644 (2017)].

    MathSciNet  MATH  Google Scholar 

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Correspondence to A. V. Pukhlikov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 299, pp. 219–233.

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Pukhlikov, A.V. Factorial Hypersurfaces. Proc. Steklov Inst. Math. 299, 205–218 (2017). https://doi.org/10.1134/S0081543817080144

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  • DOI: https://doi.org/10.1134/S0081543817080144

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