Geodesic
On automorphisms of quasi-smooth weighted complete intersections
Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 374-388 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that every reductive subgroup of the automorphism group of a quasi-smooth well-formed weighted complete intersection of dimension at least $3$ is a restriction of a subgroup in the automorphism group in the ambient weighted projective space. Also, we provide examples demonstrating that the automorphism group of a quasi-smooth well-formed Fano weighted complete intersection may be infinite and even non-reductive. Bibliography: 25 titles.
Keywords: weighted complete intersection, linear algebraic group.
Mots-clés : automorphism group 
@article{SM_2021_212_3_a7,
     author = {V. V. Przyjalkowski and {\CYRS}. A. Shramov},
     title = {On automorphisms of quasi-smooth weighted complete intersections},
     journal = {Sbornik. Mathematics},
     pages = {374--388},
     year = {2021},
     volume = {212},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_3_a7/}
}
TY  - JOUR
AU  - V. V. Przyjalkowski
AU  - С. A. Shramov
TI  - On automorphisms of quasi-smooth weighted complete intersections
JO  - Sbornik. Mathematics
PY  - 2021
SP  - 374
EP  - 388
VL  - 212
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_2021_212_3_a7/
LA  - en
ID  - SM_2021_212_3_a7
ER  - 
%0 Journal Article
%A V. V. Przyjalkowski
%A С. A. Shramov
%T On automorphisms of quasi-smooth weighted complete intersections
%J Sbornik. Mathematics
%D 2021
%P 374-388
%V 212
%N 3
%U http://geodesic.mathdoc.fr/item/SM_2021_212_3_a7/
%G en
%F SM_2021_212_3_a7
V. V. Przyjalkowski; С. A. Shramov. On automorphisms of quasi-smooth weighted complete intersections. Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 374-388. http://geodesic.mathdoc.fr/item/SM_2021_212_3_a7/

[1] A. L. Onishchik, E. B. Vinberg, Lie groups and algebraic groups, Springer Ser. Soviet Math., Springer-Verlag, Berlin, 1990, xx+328 pp. | DOI | MR | MR | Zbl | Zbl

[2] V. V. Przyjalkowski, C. A. Shramov, “Automorphisms of weighted complete intersections”, Proc. Steklov Inst. Math., 307 (2019), 198–209 | DOI | DOI | MR | Zbl

[3] V. V. Przyjalkowski, C. A. Shramov, “Fano weighted complete intersections of large codimension”, Siberian Math. J., 61:2 (2020), 298–303 | DOI | DOI | Zbl

[4] A. N. Tyurin, “On intersections of quadrics”, Russian Math. Surveys, 30:6 (1975), 51–105 | DOI | MR | Zbl

[5] C. Ciliberto, R. Lazarsfeld, “On the uniqueness of certain linear series on some classes of curves”, Complete intersections (Acireale, 1983), Lecture Notes in Math., 1092, Springer, Berlin, 1984, 198–213 | DOI | MR | Zbl

[6] A. Dimca, “Singularities and coverings of weighted complete intersections”, J. Reine Angew. Math., 1986:366 (1986), 184–193 | DOI | MR | Zbl

[7] I. Dolgachev, “Weighted projective varieties”, Group actions and vector fields (Vancouver, BC, 1981), Lecture Notes in Math., 956, Berlin, Springer, 1982, 34–71 | DOI | MR | Zbl

[8] D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995, xvi+785 pp. | DOI | MR | Zbl

[9] R. M. Fossum, The divisor class group of a Krull domain, Ergeb. Math. Grenzgeb., 74, Springer-Verlag, New York–Heidelberg, 1973, viii+148 pp. | DOI | MR | Zbl

[10] R. Hartshorne, “Complete intersections and connectedness”, Amer. J. Math., 84:3 (1962), 497–508 | DOI | MR | Zbl

[11] R. Hartshorne, “Generalized divisors on Gorenstein curves and a theorem of Noether”, J. Math. Kyoto Univ., 26:3 (1986), 375–386 | DOI | MR | Zbl

[12] A. R. Iano-Fletcher, “Working with weighted complete intersections”, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000, 101–173 | DOI | MR | Zbl

[13] Y. Kawamata, “The cone of curves of algebraic varieties”, Ann. of Math. (2), 119:3 (1984), 603–633 | DOI | MR | Zbl

[14] A. R. Mavlyutov, “Cohomology of complete intersections in toric varieties”, Pacific J. Math., 191:1 (1999), 133–144 | DOI | MR | Zbl

[15] Y. Miyaoka, S. Mori, “A numerical criterion for uniruledness”, Ann. of Math. (2), 124:1 (1986), 65–69 | DOI | MR | Zbl

[16] T. Okada, “Stable rationality of orbifold Fano 3-fold hypersurfaces”, J. Algebraic Geom., 28:1 (2019), 99–138 | DOI | MR | Zbl

[17] M. Pizzato, T. Sano, L. Tasin, “Effective nonvanishing for Fano weighted complete intersections”, Algebra Number Theory, 11:10 (2017), 2369–2395 | DOI | MR | Zbl

[18] Yu. Prokhorov, C. Shramov, “Jordan constant for Cremona group of rank 3”, Mosc. Math. J., 17:3 (2017), 457–509 | DOI | MR | Zbl

[19] V. Przyjalkowski, C. Shramov, “Bounds for smooth Fano weighted complete intersections”, Commun. Number Theory Phys., 14:3 (2020), 511–553 | DOI | MR | Zbl

[20] V. Przyjalkowski, C. Shramov, “Hodge level for weighted complete intersections”, Collect. Math., 71:3 (2020), 549–574 | DOI | MR | Zbl

[21] L. Robbiano, “Some properties of complete intersections in “good” projective varieties”, Nagoya Math. J., 61 (1976), 103–111 | DOI | MR | Zbl

[22] M. Rossi, L. Terracini, “Linear algebra and toric data of weighted projective spaces”, Rend. Semin. Mat. Univ. Politec. Torino, 70:4 (2012), 469–495 | MR | Zbl

[23] K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Notes written in collaboration with P. Cherenack, Lecture Notes in Math., 439, Springer-Verlag, Berlin–New York, 1975, xix+278 pp. | DOI | MR | Zbl

[24] K. Watanabe, “Some remarks concerning Demazure's construction of normal graded rings”, Nagoya Math. J., 83 (1981), 203–211 | DOI | MR | Zbl

[25] Qi Zhang, “Rational connectedness of $\log Q$-Fano varieties”, J. Reine Angew. Math., 2006:590 (2006), 131–142 | DOI | MR | Zbl