Ballico, Edoardo ; Bernardi, Alessandra
(2010)
On the X-rank with respect to linearly normal curves.
[Preprint]
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Abstract
In this paper we study the X-rank of points with respect to smooth linearly normal curves X contained in P^n of genus g and degree n+g.
We prove that, for such a curve X, under certain circumstances, the X-rank of a general point of X-border rank equal to s is less or equal than n+1-s.
In the particular case of g=2 we give a complete description of the X-rank if n=3,4; while if n is greter or equal than 5 we study the X-rank of points belonging to the tangential variety of X.
Abstract
In this paper we study the X-rank of points with respect to smooth linearly normal curves X contained in P^n of genus g and degree n+g.
We prove that, for such a curve X, under certain circumstances, the X-rank of a general point of X-border rank equal to s is less or equal than n+1-s.
In the particular case of g=2 we give a complete description of the X-rank if n=3,4; while if n is greter or equal than 5 we study the X-rank of points belonging to the tangential variety of X.
Document type
Preprint
Creators
Additional Information
The authors were partially supported by CIRM - FBK (TN - Italy), MIUR and GNSAGA of INdAM (Italy).
Keywords
Secant varieties, Tangential varieties, Rank, Linearly normal curves.
Subjects
DOI
Deposit date
09 Feb 2010 14:04
Last modified
16 May 2011 12:13
URI
Other metadata
Document type
Preprint
Creators
Additional Information
The authors were partially supported by CIRM - FBK (TN - Italy), MIUR and GNSAGA of INdAM (Italy).
Keywords
Secant varieties, Tangential varieties, Rank, Linearly normal curves.
Subjects
DOI
Deposit date
09 Feb 2010 14:04
Last modified
16 May 2011 12:13
URI
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