Geodesic
On the connectedness of the automorphism group of an affine toric variety
Sbornik. Mathematics, Tome 215 (2024) no. 10, pp. 1351-1373 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain a criterion for the automorphism group of an affine toric variety to be connected, stated in combinatorial terms and in terms of the divisor class group of the variety. We describe the component group of the automorphism group of a nondegenerate affine toric variety. In particular, we show that the number of connected components of the automorphism group is finite. Bibliography: 12 titles.
Keywords: toric variety, divisor class group, Cox ring.
Mots-clés : automorphism group 
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V. V. Kikteva. On the connectedness of the automorphism group of an affine toric variety. Sbornik. Mathematics, Tome 215 (2024) no. 10, pp. 1351-1373. http://geodesic.mathdoc.fr/item/SM_2024_215_10_a2/

[1] C. P. Ramanujam, “A note on automorphism groups of algebraic varieties”, Math. Ann., 156 (1964), 25–33 | DOI | MR | Zbl

[2] V. L. Popov, “On infinite dimensional algebraic transformation groups”, Transform. Groups, 19:2 (2014), 549–568 | DOI | MR | Zbl

[3] I. V. Arzhantsev and S. A. Gaifullin, “Cox rings, semigroups and automorphisms of affine algebraic varieties”, Sb. Math., 201:1 (2010), 1–21 | DOI | MR | Zbl

[4] D. Cox, “The homogeneous coordinate ring of a toric variety”, J. Algebraic Geom., 4:1 (1995), 17–50 | MR | Zbl

[5] M. Demazure, “Sous-groupes algébriques de rang maximum du groupe de Cremona”, Ann. Sci. Éc. Norm. Supér. (4), 3:4 (1970), 507–588 | DOI | MR | Zbl

[6] I. R. Šafarevič (Shafarevich), “On some infinite-dimensional groups. II”, Math. USSR-Izv., 18:1 (1982), 185–194 | DOI | MR | Zbl

[7] D. A. Cox, J. B. Little and H. K. Schenck, Toric varieties, Grad. Stud. Math., 124, Amer. Math. Soc., Providence, RI, 2011, xxiv+841 pp. | DOI | MR | Zbl

[8] W. Fulton, Introduction to toric varieties, Ann. of Math. Stud., 131, William Roever Lectures Geom., Princeton Univ. Press, Princeton, NJ, 1993, xii+157 pp. | DOI | MR | Zbl

[9] I. R. Shafarevich, Basic algebraic geometry, v. 1, Varieties in projective space, 3rd ed., Springer, Heidelberg, 2013, xviii+310 pp. ; v. 2, Schemes and complex manifolds, 3rd ed., 2013, xiv+262 pp. | DOI | MR | Zbl | DOI | MR | Zbl

[10] I. Arzhantsev and I. Bazhov, “On orbits of the automorphism group on an affine toric variety”, Cent. Eur. J. Math., 11:10 (2013), 1713–1724 | DOI | MR | Zbl

[11] I. Arzhantsev, U. Derenthal, J. Hausen and A. Laface, Cox rings, Cambridge Stud. Adv. Math., 144, Cambridge Univ. Press, Cambridge, 2015, viii+530 pp. | DOI | MR | Zbl

[12] I. Arzhantsev and M. Zaidenberg, “Acyclic curves and group actions on affine toric surfaces”, Affine algebraic geometry (Osaka 2011), World Sci. Publ., Hackensack, NJ, 2013, 1–41 | DOI | MR | Zbl