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EnglishLet $X\subset\P^N$ be a smooth variety. The embedding in $\P^n$ gives naturally rise to the notion of embedded tangent spaces. That is the locus spanned by tangent lines to a point $x\in X$. Generally the embedded tangent space intersects the variety $X$ only at the point $x$. In this paper I am interested in those $X$ for which this intersection, for $x\in X$ general, is a positive dimensional subvariety. The results of this paper support the conjecture that these varieties are built out of some special varieties that I call {\sl Tangentially Connected}, see Definition \ref{def:TC}. Actually I prove this under mild restrictions.
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| Data di pubblicazione: | 2009 | |
| Titolo: | Tangential Connection | |
| Autori: | Mella M. | |
| Rivista: | ADVANCES IN GEOMETRY | |
| Parole Chiave: | embedded tangent space; algebraic equivalence relation | |
| Abstract: | Let $X\subset\P^N$ be a smooth variety. The embedding in $\P^n$ gives naturally rise to the notion of embedded tangent spaces. That is the locus spanned by tangent lines to a point $x\in X$. Generally the embedded tangent space intersects the variety $X$ only at the point $x$. In this paper I am interested in those $X$ for which this intersection, for $x\in X$ general, is a positive dimensional subvariety. The results of this paper support the conjecture that these varieties are built out of some special varieties that I call {\sl Tangentially Connected}, see Definition \ref{def:TC}. Actually I prove this under mild restrictions. | |
| Digital Object Identifier (DOI): | 10.1515/ADVGEOM.2009.023 | |
| Handle: | http://hdl.handle.net/11392/518072 | |
| Appare nelle tipologie: | 03.1 Articolo su rivista |
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