@article{TM_2016_294_a9,
author = {Victor V. Przyjalkowski and Constantin A. Shramov},
title = {Double quadrics with large automorphism groups},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {167--190},
year = {2016},
volume = {294},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2016_294_a9/}
}
Victor V. Przyjalkowski; Constantin A. Shramov. Double quadrics with large automorphism groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 167-190. http://geodesic.mathdoc.fr/item/TM_2016_294_a9/
[1] Artin M., Mumford D., “Some elementary examples of unirational varieties which are not rational”, Proc. London Math. Soc. Ser. 3, 25 (1972), 75–95 | DOI | MR | Zbl
[2] Aspinwall P. S., Morrison D. R., “Stable singularities in string theory (with an appendix by M. Gross)”, Commun. Math. Phys., 178:1 (1996), 115–134 | DOI | MR | Zbl
[3] Beauville A., “Variétés de Prym et jacobiennes intermediaires”, Ann. sci. Éc. Norm. Supér. Sér. 4, 10 (1977), 309–391 | MR | Zbl
[4] Beauville A., “Non-rationality of the $\mathfrak S_6$-symmetric quartic threefolds”, Rend. Semin. Mat. Univ. Politec. Torino, 71 (2013), 385–388 | MR | Zbl
[5] Burkhardt H., “Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunctionen. Zweiter Theil”, Math. Ann., 38 (1891), 161–224 | DOI | MR
[6] Cheltsov I., Przyjalkowski V., Shramov C., “Quartic double solids with icosahedral symmetry”, Eur. J. Math., 2:1 (2016), 96–119 | DOI | MR | Zbl
[7] Cheltsov I., Shramov C., Two rational nodal quartic threefolds, E-print, 2015, arXiv: 1511.07508[math.AG]
[8] Cheltsov I., Shramov C., Cremona groups and the icosahedron, CRC Press, Boca Raton, FL, 2016 | MR | Zbl
[9] Colliot-Thélène J.-L., Pirutka A., “Hypersurfaces quartiques de dimension 3: non-rationalité stable”, Ann. sci. Éc. Norm. Supér. Sér. 4, 49:2 (2016), 371–397 | MR | Zbl
[10] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., Atlas of finite groups: Maximal subgroups and ordinary characters for simple groups, Clarendon Press, Oxford, 1985 | MR | Zbl
[11] Cynk S., “Defect of a nodal hypersurface”, Manuscr. math., 104:3 (2001), 325–331 | DOI | MR | Zbl
[12] Feit W., “The current situation in the theory of finite simple groups”, Actes Congr. int. math. (Nice, 1970), v. 1, Gauthier-Villars, Paris, 1971, 55–93 | MR
[13] Gorchinskii S. O., Shramov K. A., Nerazvetvlennaya gruppa Brauera i ee prilozheniya, E-print, 2015, arXiv: 1512.00874[math.AG]
[14] Grinenko M. M., “Biratsionalnye avtomorfizmy trekhmernoi dvoinoi kvadriki s prosteishei osobennostyu”, Mat. sb., 189:1 (1998), 101–118 | DOI | MR | Zbl
[15] Grinenko M. M., “Biratsionalnye avtomorfizmy trekhmernogo dvoinogo konusa”, Mat. sb., 189:7 (1998), 37–52 | DOI | MR | Zbl
[16] Hassett B., Tschinkel Yu., On stable rationality of Fano threefolds and del Pezzo fibrations, E-print, 2016, arXiv: 1601.07074[math.AG]
[17] Iliev A., Katzakov L., Przyjalkowski V., “Double solids, categories and non-rationality”, Proc. Edinburgh Math. Soc. Ser. 2, 57:1 (2014), 145–173 | DOI | MR | Zbl
[18] Iskovskikh V. A., Prokhorov Yu. G., Fano varieties, Encycl. Math. Sci., 47, Springer, Berlin, 1999 | MR | Zbl
[19] Iskovskikh V. A., Pukhlikov A. V., “Biratsionalnye avtomorfizmy mnogomernykh algebraicheskikh mnogoobrazii”, Algebraicheskaya geometriya – 1, Itogi nauki i tekhniki. Sovr. matematika i ee pril. Tematich. obzory, 19, VINITI, M., 2001, 5–139 | MR | Zbl
[20] Klein F., “Ueber die Transformation siebenter Ordnung der elliptischen Functionen”, Math. Ann., 14 (1879), 428–471 | DOI | MR
[21] Kuznetsov A. G., “O mnogoobraziyakh Kyukhle s chislom Pikara, bolshim 1”, Izv. RAN. Ser. mat., 79:4 (2015), 57–70 | DOI | MR | Zbl
[22] Pettersen K., On nodal determinantal quartic hypersurfaces in $\mathbb P^4$, PhD Thesis, Univ. Oslo, Oslo, 1998
[23] Prokhorov Yu., “Simple finite subgroups of the Cremona group of rank 3”, J. Algebr. Geom., 21:3 (2012), 563–600 | DOI | MR | Zbl
[24] Prokhorov Yu. G., “O trekhmernykh $G$-mnogoobraziyakh Fano”, Izv. RAN. Ser. mat., 79:4 (2015), 159–174 | DOI | MR | Zbl
[25] Prokhorov Yu. G., “Osobye mnogoobraziya Fano roda 12”, Mat. sb., 207:7 (2016), 101–130 | DOI | MR
[26] Prokhorov Yu. G., “Trekhmernye mnogoobraziya $\mathbb Q$-Fano indeksa 7”, Tr. MIAN, 294, 2016, 152–166 | DOI
[27] Pukhlikov A. V., “Biratsionalnye avtomorfizmy dvoinogo prostranstva i dvoinoi kvadriki”, Izv. AN SSSR. Ser. mat., 52:1 (1988), 229–239 | MR | Zbl
[28] Schreieder S., Tasin L., A very general quartic or quintic fivefold is not stably rational, E-print, 2015, arXiv: 1510.02011v2[math.AG]
[29] Shramov K. A., “O biratsionalnoi zhestkosti i $\mathbb Q$-faktorialnosti osobogo dvoinogo nakrytiya kvadriki s vetvleniem v divizore stepeni 4”, Mat. zametki, 84:2 (2008), 300–311 | DOI | MR | Zbl
[30] Todd J. A., “Configurations defined by six lines in space of three dimensions”, Proc. Cambridge Philos. Soc., 29 (1933), 52–68 | DOI | Zbl
[31] Todd J. A., “A note on two special primals in four dimensions”, Q. J. Math., 6 (1935), 129–136 | DOI | Zbl
[32] Todd J. A., “On a quartic primal with forty-five nodes, in space of four dimensions”, Q. J. Math., 7 (1936), 168–174 | DOI | Zbl
[33] Voisin C., Hodge theory and complex algebraic geometry, v. I, Cambridge Stud. Adv. Math., 76, Cambridge Univ. Press, Cambridge, 2007 | MR | Zbl
[34] Voisin C., “Unirational threefolds with no universal codimension 2 cycle”, Invent. math., 201:1 (2015), 207–237 | DOI | MR | Zbl