Geodesic
Factorial hypersurfaces
Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 219-233.

Voir la notice de l'article provenant de la source Math-Net.Ru

The codimension of the complement of the set of factorial hypersurfaces of degree $d$ in $\mathbb P^N$ is estimated for $d\geq 4$ and $N\geq 7$.
Keywords: factoriality, singularity.
Mots-clés : hypersurface 
@article{TRSPY_2017_299_a13,
     author = {A. V. Pukhlikov},
     title = {Factorial hypersurfaces},
     journal = {Informatics and Automation},
     pages = {219--233},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a13/}
}
TY  - JOUR
AU  - A. V. Pukhlikov
TI  - Factorial hypersurfaces
JO  - Informatics and Automation
PY  - 2017
SP  - 219
EP  - 233
VL  - 299
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a13/
LA  - ru
ID  - TRSPY_2017_299_a13
ER  - 
%0 Journal Article
%A A. V. Pukhlikov
%T Factorial hypersurfaces
%J Informatics and Automation
%D 2017
%P 219-233
%V 299
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a13/
%G ru
%F TRSPY_2017_299_a13
A. V. Pukhlikov. Factorial hypersurfaces. Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 219-233. http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a13/

[1] Call F., Lyubeznik G., “A simple proof of Grothendieck's theorem on the parafactoriality of local rings”, Commutative algebra: Syzygies, multiplicities, and birational algebra, Contemp. Math., 159, Amer. Math. Soc., Providence, RI, 1994, 15–18 | DOI | MR | Zbl

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

[3] Cheltsov I., “Factorial threefold hypersurfaces”, J. Algebr. Geom., 19:4 (2010), 781–791 | DOI | MR | Zbl

[4] Cheltsov I., Park J., “Factorial hypersurfaces in $\mathbb P^4$ with nodes”, Geom. dedicata, 121 (2006), 205–219 | DOI | MR | Zbl

[5] Ciliberto C., Di Gennaro V., “Factoriality of certain threefolds complete intersection in $\mathbb P^5$ with ordinary double points”, Commun. Algebra, 32:7 (2004), 2705–2710 | DOI | MR | Zbl

[6] Mella M., “Birational geometry of quartic 3-folds. II: The importance of being $\mathbb Q$-factorial”, Math. Ann., 330:1 (2004), 107–126 | DOI | MR | Zbl

[7] Polizzi F., Rapagnetta A., Sabatino P., “On factoriality of threefolds with isolated singularities”, Mich. Math. J., 63:4 (2014), 781–801 | DOI | MR | Zbl

[8] Pukhlikov A.V., “Birational automorphisms of Fano hypersurfaces”, Invent. math., 134:2 (1998), 401–426 | DOI | MR | Zbl

[9] Pukhlikov A.V., “Birationally rigid Fano complete intersections”, J. reine angew. Math., 541 (2001), 55–79 | MR | Zbl

[10] Pukhlikov A., Birationally rigid varieties, Math. Surv. Monogr., 190, Amer. Math. Soc., Providence, RI, 2013 | DOI | MR | Zbl

[11] Pukhlikov A.V., “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1–2 (2016), 721–782 | DOI | MR | Zbl

[12] A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81 (2017), 618–644 | DOI | DOI | MR | Zbl