COHOMOLOGICAL RIGIDITY FOR TORIC FANO MANIFOLDS OF SMALL DIMENSIONS OR LARGE PICARD NUMBERS

[1] B. Assarf, M. Joswig and A. Paffenholz: Smooth Fano polytopes with many vertices, Discrete Comput. Geom. 52 (2014), 153–194.

[2] V.V. Batyrev: On the classification of smooth projective toric varieties, Tohoku Math J. 43 (1991), 569–585.

[3] V.V. Batyrev: On the classification of toric Fano 4-folds, J. Math. Sci. (New York) 94 (1999), 1021–1050.

[4] W. Bosma, J. Cannon and C. Playoust: The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), 235–265.

[5] V. Buchstaber and T. Panov: Toric Topology, Mathematical Surveys and Monographs 204, American Math- ematical Society, Providence, RI, 2015.

[6] V.M. Buchstaber, N.Yu. Erokhovets, M. Masuda, T.E. Panov and S. Park: Cohomological rigidity of mani- folds defined by 3-dimensional polytopes, Uspekhi Mat. Nauk 72 (2017), 3–66.

[7] C. Casagrande: The number of vertices of a Fano polytope, Ann. Inst. Fourier 56 (2006), 121–130.

[8] Y. Cho, E. Lee, M. Masuda and S. Park: Unique toric structure on a Fano Bott manifold, arXiv:2005.02740.

[9] S. Choi: Classification of Bott manifolds up to dimension 8, Proc. Edinb. Math. Soc. 58 (2015), 653–659.

[10] S. Choi, M. Masuda and S. Murai: Invariance of Pontrjagin classes for Bott manifolds, Algebr. Geom. Topol. 15 (2015), 965–986.

[11] S. Choi, M. Masuda and D.Y. Suh: Quasitoric manifolds over a product of simplices, Osaka J. Math. 47 (2010), 109–129.

[12] S. Choi, M. Masuda and D.Y. Suh: Topological classification of generalized Bott towers, Trans. Amer. Math. Soc. 362 (2010), 1097–1112.

[13] S. Choi, M. Masuda and D.Y. Suh: Rigidity problems in toric topology: a survey, Proc. Steklov Inst. Math. 275 (2011), 177–190.

[14] M.W. Davis: When are two Coxeter orbifolds diffeomorphic?, Michigan Math. J. 63 (2014), 401–421.

[15] M.W. Davis and T. Januszkiewicz: Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), 417–451.

[16] W. Fulton: Introduction to Toric Varieties, Ann. of Math. Studies 131, Princeton Univ. Press, Princeton, NJ, 1993.

[17] S. Hasui, H. Kuwata, M. Masuda and S. Park: Classification of toric manifolds over an n-cube with one vertex cut, Int. Math. Res. Not. IMRN (2020), 4890–4941.

[18] M. Masuda: Equivariant cohomology distinguishes toric manifolds, Adv. Math. 218 (2008), 2005–2012.

[19] M. Masuda and T. Panov: Semi-free circle actions, Bott towers, and quasitoric manifolds, Mat. Sb. 199 (2008), 95–122.

[20] M. Masuda and D.Y. Suh: Classification problems of toric manifolds via topology; in Toric topology, Contemp. Math. 460, Amer. Math. Soc., Providence, RI, 2008, 273–286.

[21] M. Øbro: An algorithm for the classification of smooth Fano polytopes, arXiv:0704.0049v1.

[22] M. Øbro: Classification of terminal simplicial reflexive d-polytopes with 3d − 1 vertices. Manuscripta. Math. 125 (2008), 69–79.

[23] T. Oda: Convex Bodies and Algebraic Geometry -An introduction to the theory of toric varieties Ergeb. Math. Grenzgeb. (3) 15, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988.

[24] H. Sato: Towards the classification of higher-dimensional toric Fano varieties, Tohoku Math J. 52 (2000), 383–413.

[25] B. Sturmfels: Gro¨bner Bases and Convex Polytopes, University Lecture Series 8, American Mathematical Society, Providence, RI, 1995.

[26] K. Watanabe and M. Watanabe: The classification of Fano 3-folds with torus embeddings, Tokyo J. Math. 5 (1982), 37–48.