Threefolds with degenerate secant variety: On a theorem of G. Scorza. (Q2717166)
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scientific article; zbMATH DE number 1604745
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Threefolds with degenerate secant variety: On a theorem of G. Scorza. |
scientific article; zbMATH DE number 1604745 |
Statements
18 September 2001
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\(k\)-defect
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classification of threefolds
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Threefolds with degenerate secant variety: On a theorem of G. Scorza. (English)
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Let \(X\) be a projective variety of dimension \(n\) in \(\mathbb{P}^n\). \(X\) is said to be \(k\)-defective if the dimension of its \(k\)-secant variety is strictly less than the expected one \(\min(r,n(k+ 1)+ k)\). The difference between these dimensions is called \(k\)-defect. In line with Scorza's results [\textit{G. Scorza}, Ann. Mat. (3) 15, 217--273 (1908; JFM 39.0717.01)], the authors rework the classification of (non-necessarily smooth) threefolds having non-zero 1-defect. The main tool to work out such results is a famous lemma by Terracini.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00042].
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