Hard Lefschetz theorem for simple polytopes
This paper contains a new original proof of the Hard Lefschetz theorem for simple polytopes, which follows the main steps of McMullen's proof and uses conewise polynomial functions on a simplicial fan [cf. \textit{L.~Billera} and \textit{C.~W.~Lee} [J. Comb. Theory, Ser. A 31, 237--255 (1981; Zbl 0479.52006); \textit{P.~McMullen}, Invent. Math. 113, No.~2, 419--444 (1993; Zbl 0803.52007); \textit{R.~Stanley}, Adv. Math. 35, 236--238 (1980; Zbl 0427.52006); \textit{V. A.~Timorin}, Russ. Math. Surv. 54, No.~2, 381--426 (1999); translation from Usp. Mat. Nauk 54, No.~2, 113--162 (1999; Zbl 0944.52005)].
scientific article; zbMATH DE number 5824575