Automorphisms of Weighted Complete Intersections
Informatics and Automation, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 217-229.

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We show that smooth well-formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.
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Victor V. Przyjalkowski; Constantin A. Shramov. Automorphisms of Weighted Complete Intersections. Informatics and Automation, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 217-229. http://geodesic.mathdoc.fr/item/TRSPY_2019_307_a11/

[1] Araujo C., Corrêa M., Massarenti A., “Codimension one Fano distributions on Fano manifolds”, Commun. Contemp. Math., 20:5 (2018), 1750058 | DOI | MR | Zbl

[2] Benoist O., “Séparation et propriété de Deligne–Mumford des champs de modules d'intersections complètes lisses”, J. London Math. Soc. Ser. 2, 87:1 (2013), 138–156 | DOI | MR | Zbl

[3] A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York, 1969 | MR | Zbl

[4] Cheltsov I., Shramov C., Cremona groups and the icosahedron, Monogr. Res. Notes Math., CRC Press, Boca Raton, FL, 2016 | MR | Zbl

[5] Chen J.-J., Chen J.A., Chen M., “On quasismooth weighted complete intersections”, J. Algebr. Geom., 20:2 (2011), 239–262 | DOI | MR | Zbl

[6] Dolgachev I., “Weighted projective varieties”, Group actions and vector fields, Proc. Pol.–North Amer. Semin. (Vancouver, 1981), Lect. Notes Math., 956, Springer, Berlin, 1982, 34–71 | DOI | MR

[7] Dolgachev I.V., Classical algebraic geometry: A modern view, Cambridge Univ. Press, Cambridge, 2012 | MR | Zbl

[8] Flenner H., “Divisorenklassengruppen quasihomogener Singularitäten”, J. reine angew. Math., 328 (1981), 128–160 | MR | Zbl

[9] Fujita T., “On the structure of polarized manifolds with total deficiency one. I”, J. Math. Soc. Japan, 32 (1980), 709–725 | DOI | MR | Zbl

[10] Fujita T., “On the structure of polarized manifolds with total deficiency one. II”, J. Math. Soc. Japan, 33 (1981), 415–434 | DOI | MR | Zbl

[11] Fujita T., “On the structure of polarized manifolds with total deficiency one. III”, J. Math. Soc. Japan, 36 (1984), 75–89 | DOI | MR | Zbl

[12] Hacon C.D., McKernan J., Xu C., “On the birational automorphisms of varieties of general type”, Ann. Math. Ser. 2, 177:3 (2013), 1077–1111 | DOI | MR | Zbl

[13] Hartshorne R., Local cohomology: A seminar given by A. Grothendieck (Harvard Univ., Fall, 1961), Lect. Notes Math., 41, Springer, Berlin, 1967 | DOI | MR | Zbl

[14] R. Hartshorne, Algebraic Geometry, Grad. Texts Math., 52, Springer, New York, 1977 | DOI | MR | Zbl

[15] Iano-Fletcher A.R., “Working with weighted complete intersections”, Explicit birational geometry of 3-folds, LMS Lect. Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000, 101–173 | MR | Zbl

[16] Iskovskikh V.A., Prokhorov Yu.G., Fano varieties, Encycl. Math. Sci., 47, Springer, Berlin, 1999 | MR | Zbl

[17] Kodaira K., Spencer D.C., “On deformations of complex analytic structures. II”, Ann. Math. Ser. 2, 67:3 (1958), 403–466 | DOI | MR | Zbl

[18] Kuznetsov A.G., Prokhorov Yu.G., Shramov C.A., “Hilbert schemes of lines and conics and automorphism groups of Fano threefolds”, Jpn. J. Math., 13:1 (2018), 109–185 | DOI | MR | Zbl

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

[20] Matsumura H., Monsky P., “On the automorphisms of hypersurfaces”, J. Math. Kyoto Univ., 3 (1964), 347–361 | DOI | MR | Zbl

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

[22] Mori S., “On a generalization of complete intersections”, J. Math. Kyoto Univ., 15:3 (1975), 619–646 | DOI | MR | Zbl

[23] Mukai S., “Curves, K3 surfaces and Fano 3-folds of genus $\leq 10$”, Algebraic geometry and commutative algebra, In honor of M. Nagata, v. I, Konokuniya, Tokyo, 1988, 357–377 | MR

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

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

[26] V. V. Przyjalkowski, I. A. Cheltsov, and C. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907 | DOI | DOI | MR | Zbl

[27] Przyjalkowski V., Shramov C., Bounds for smooth Fano weighted complete intersections, E-print, 2016, arXiv: 1611.09556 [math.AG]

[28] Przyjalkowski V., Shramov C., “Hodge level for weighted complete intersections”, Collect. Math., 2020 ; arXiv: 1801.10489v2 [math.AG] | DOI