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- W2465057733 abstract "We survey, following Fulton, the connectedness principle of Enriques–Severi–Zariski claiming that limits of irreducible varieties remain connected. Some deep generalizations are reported following the circle of ideas which led to the Connectedness Theorem of Fulton–Hansen and to some new results related to it. We include a proof of the Fulton–Hansen Theorem according to Deligne and we describe its consequences for the geometry of embedded projective varieties proved by Zak: Theorem on Tangency, finiteness of the Gauss map, dimension of the dual variety, hyperplane sections of low-codimensional varieties. These are modern and deep generalizations of many classical theorems in projective geometry which usually dealt with general objects. We also define some classical tangential invariants of projective varieties and connect them to tangential projections and to Scorza’s Lemma. Then we consider the well-known characterization of the Veronese surface, due to Severi, as the unique non-degenerate surface in (mathbb{P}^{N}), N ≥ 5, not a cone and with (dim (SX) = 4). The novelty of our proof of this result and of its generalization to arbitrary dimension in Theorem 3.4.4 relies on a complete parallel with Mori’s proof of the characterization of the projective space as the unique manifold with ample tangent bundle." @default.
- W2465057733 created "2016-07-22" @default.
- W2465057733 creator A5060692499 @default.
- W2465057733 date "2016-01-01" @default.
- W2465057733 modified "2023-09-27" @default.
- W2465057733 title "The Fulton–Hansen Connectedness Theorem, Scorza’s Lemma and Their Applications to Projective Geometry" @default.
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- W2465057733 doi "https://doi.org/10.1007/978-3-319-26765-4_3" @default.
- W2465057733 hasPublicationYear "2016" @default.
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