Geodesic
$c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 368-381 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The $c_1$-cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a $c_1$-preserving isomorphism between their integral cohomology rings. In this paper, we confirm the conjecture for smooth toric Fano varieties of Picard number $2$.
Keywords: $c_1$-cohomological rigidity, toric Fano varieties, generalized Bott manifolds. 
@article{TRSPY_2024_326_a15,
     author = {Yunhyung Cho and Eunjeong Lee and Mikiya Masuda and Seonjeong Park},
     title = {$c_1${-Cohomological} {Rigidity} for {Smooth} {Toric} {Fano} {Varieties} of {Picard} {Number} {Two}},
     journal = {Informatics and Automation},
     pages = {368--381},
     year = {2024},
     volume = {326},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a15/}
}
TY  - JOUR
AU  - Yunhyung Cho
AU  - Eunjeong Lee
AU  - Mikiya Masuda
AU  - Seonjeong Park
TI  - $c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
JO  - Informatics and Automation
PY  - 2024
SP  - 368
EP  - 381
VL  - 326
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a15/
LA  - ru
ID  - TRSPY_2024_326_a15
ER  - 
%0 Journal Article
%A Yunhyung Cho
%A Eunjeong Lee
%A Mikiya Masuda
%A Seonjeong Park
%T $c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
%J Informatics and Automation
%D 2024
%P 368-381
%V 326
%U http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a15/
%G ru
%F TRSPY_2024_326_a15
Yunhyung Cho; Eunjeong Lee; Mikiya Masuda; Seonjeong Park. $c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two. Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 368-381. http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a15/

[1] Batyrev V.V., “On the classification of smooth projective toric varieties”, Tôhoku Math. J. Ser. 2, 43:4 (1991), 569–585 | DOI | MR | Zbl

[2] Batyrev V.V., “On the classification of toric Fano 4-folds”, J. Math. Sci., 94 (1999), 1021–1050 | DOI | MR | Zbl

[3] V. M. Buchstaber, N. Yu. Erokhovets, M. Masuda, T. E. Panov, and S. Park, “Cohomological rigidity of manifolds defined by 3-dimensional polytopes”, Russ. Math. Surv., 72:2 (2017), 199–256 | DOI | DOI | MR | Zbl

[4] Buchstaber V.M., Panov T.E., Toric topology, Math. Surv. Monogr., 204, Am. Math. Soc., Providence, RI, 2015 | DOI | MR | Zbl

[5] Cho Y., Lee E., Masuda M., Park S., “Unique toric structure on a Fano Bott manifold”, J. Symplectic Geom., 21:3 (2023), 439–462 | DOI | MR | Zbl

[6] Choi S., Hwang T., Jang H., Strong cohomological rigidity of Bott manifolds, E-print, 2022, arXiv: 2202.10920 [math.AT] | DOI

[7] Choi S., Masuda M., Oum S., “Classification of real Bott manifolds and acyclic digraphs”, Trans. Am. Math. Soc., 369:4 (2017), 2987–3011 | DOI | MR | Zbl

[8] Choi S., Masuda M., Suh D.Y., “Topological classification of generalized Bott towers”, Trans. Am. Math. Soc., 362:2 (2010), 1097–1112 | DOI | MR | Zbl

[9] Choi S., Panov T.E., Suh D.Y., “Toric cohomological rigidity of simple convex polytopes”, J. London Math. Soc. Ser. 2, 82:2 (2010), 343–360 | DOI | MR | Zbl

[10] Choi S., Park S., “Projective bundles over toric surfaces”, Int. J. Math., 27:4 (2016), 1650032 | DOI | MR | Zbl

[11] Choi S., Park S., Suh D.Y., “Topological classification of quasitoric manifolds with second Betti number 2”, Pac. J. Math., 256:1 (2012), 19–49 | DOI | MR | Zbl

[12] Cox D.A., Little J.B., Schenck H.K., Toric varieties, Grad. Stud. Math., 124, Am. Math. Soc., Providence, RI, 2011 | DOI | MR | Zbl

[13] Davis M.W., Januszkiewicz T., “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 | DOI | MR | Zbl

[14] Delzant T., “Hamiltoniens périodiques et images convexes de l'application moment”, Bull. Soc. math. France, 116:3 (1988), 315–339 | DOI | MR | Zbl

[15] Fanoe A., “Toric structures on bundles of projective spaces”, J. Symplectic Geom., 12:4 (2014), 685–724 | DOI | MR | Zbl

[16] Hasui S., Kuwata H., Masuda M., Park S., “Classification of toric manifolds over an $n$-cube with one vertex cut”, Int. Math. Res. Not., 2020:16 (2020), 4890–4941 | DOI | MR | Zbl

[17] Higashitani A., Kurimoto K., Masuda M., “Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers”, Osaka J. Math., 59:1 (2022), 177–215 | MR | Zbl

[18] Kamishima Y., Masuda M., “Cohomological rigidity of real Bott manifolds”, Algebr. Geom. Topol., 9:4 (2009), 2479–2502 | DOI | MR | Zbl

[19] Kleinschmidt P., “A classification of toric varieties with few generators”, Aequationes math., 35:2–3 (1988), 254–266 | DOI | MR | Zbl

[20] Masuda M., “Equivariant cohomology distinguishes toric manifolds”, Adv. Math., 218:6 (2008), 2005–2012 | DOI | MR | Zbl

[21] M. Masuda, “Cohomological non-rigidity of generalized real Bott manifolds of height 2”, Proc. Steklov Inst. Math., 268 (2010), 242–247 | DOI | MR | Zbl

[22] Masuda M., Suh D.Y., “Classification problems of toric manifolds via topology”, Toric topology: Int. Conf., Osaka, 2006, Contemp. Math., 460, Am. Math. Soc., Providence, RI, 2008, 273–286 | DOI | MR | Zbl

[23] McDuff D., “The topology of toric symplectic manifolds”, Geom. Topol., 15:1 (2011), 145–190 | DOI | MR | Zbl

[24] Oda T., Convex bodies and algebraic geometry: An introduction to the theory of toric varieties, Ergeb. Math. Grenzgeb. 3. Folge, 15, Springer, Berlin, 1988 | MR | Zbl

[25] Suyama Y., “Fano generalized Bott manifolds”, Manuscr. math., 163:3–4 (2020), 427–435 | DOI | MR | Zbl

[26] Øbro M., An algorithm for the classification of smooth fano polytopes, E-print, 2007, arXiv: 0704.0049 [math.CO] | DOI