The Togliatti surface (Q2702167)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Togliatti surface |
scientific article |
Statements
2 April 2001
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osculating spaces
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JFM 55.1011.02
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Del Pezzo surface of degree 6
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The Togliatti surface (English)
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The first example of a complex smooth surface in \(\mathbb{P}^5\) that is not a scroll and such that all its second osculating spaces have dimension less than expected was discovered by \textit{E. G. Togliatti} in 1929 [Comment. Math. Helvet. 1, 255-272 (1929; JFM 55.1011.02)]. It is the isomorphic image of the Del Pezzo surface of degree 6 of \(\mathbb{P}^6\) via the projection from a very special point. In this survey paper the author discusses this interesting example in connection with several recent papers in projective differential geometry.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00066].
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