Inflections of toric varieties. (Q5954574)

The study of the inflectional behavior of varieties is a classical topic in algebraic geometry. In the paper under review, the author investigates in detail the case ofNEWLINEsmooth projective toric varieties \(X\), embedded by a toric map \(v: X\to \mathbb{P}^n\) into the projective space. By restricting himself to the toric case, he is able to decribeNEWLINEthe inflectional behavior of \(v\) by combinatorial methods, in terms of the associated polytope. He gives a complete classification in the case of embedded toric surfaces and threefolds with the property that for every point \(p\) of \(X\), the \(k\)-th osculating spaces of \(v\) at \(p\) are as big as possible for \(k=1,\dots ,s-1\) NEWLINEand strictly smaller for \(k=s\). Furthermore, he applies his methods to reproof theorems of \textit{W. Fulton}, \textit{S. Kleiman}, \textit{R. Piene}, and \textit{H. Tai} [Bull. Soc. Math. Fr. 113, 205--210 (1985; Zbl 0581.14037)] and \textit{E. Ballico, R. Piene}, and \textit{H. Tai} [Math. Scand. 70, No.2, 204--206 (1992; Zbl 0778.14017)] in the toric case.