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.
Similar content being viewed by others
References
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.
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)].
I. Cheltsov, “Factorial threefold hypersurfaces,” J. Algebr. Geom. 19 (4), 781–791 (2010).
I. Cheltsov and J. Park, “Factorial hypersurfaces in P4 with nodes,” Geom. Dedicata 121, 205–219 (2006).
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).
M. Mella, “Birational geometry of quartic 3-folds. II: The importance of being Q-factorial,” Math. Ann. 330 (1), 107–126 (2004).
F. Polizzi, A. Rapagnetta, and P. Sabatino, “On factoriality of threefolds with isolated singularities,” Mich. Math. J. 63 (4), 781–801 (2014).
A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces,” Invent. Math. 134 (2), 401–426 (1998).
A. V. Pukhlikov, “Birationally rigid Fano complete intersections,” J. Reine Angew. Math. 541, 55–79 (2001).
A. Pukhlikov, Birationally Rigid Varieties (Am. Math. Soc., Providence, RI, 2013), Math. Surv. Monogr. 190.
A. V. Pukhlikov, “Birational geometry of Fano hypersurfaces of index two,” Math. Ann. 366 (1–2), 721–782 (2016).
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)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 299, pp. 219–233.
Rights and permissions
About this article
Cite this article
Pukhlikov, A.V. Factorial Hypersurfaces. Proc. Steklov Inst. Math. 299, 205–218 (2017). https://doi.org/10.1134/S0081543817080144
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543817080144