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Results tagged with projective-varieties
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user 14514
In algebraic geometry, a projective variety over an algebraically closed field $k$ is a subset of some projective $n$-space $\mathbb P^n$ over $k$ that is the zero-locus of some finite family of homogeneous polynomials of $n + 1$ variables with coefficients in $k$, that generate a prime ideal, the defining ideal of the variety
12
votes
Accepted
Degree of secant varieties of Veronese varieties
The secant variety $Sec_k(V^n_2)$ is the variety parametrizing $(n+1)\times (n+1)$ symmetric matrices modulo scalar of rank at most $k$ that is of corank at least $n+1-k$.
Then by Proposition 12(b) in …
- 8,998
2
votes
Varieties with few trisecant lines
Assume that $X$ is set theoretically defined by quadrics: $ X = Q_1\cap\dots\cap Q_r$.
If $L$ is a line trisecant to $X$ then $L$ is trisecant to $Q_i$ for all $i$ and hence $L\subset Q_i$ for all $i$ …
- 8,998
0
votes
Accepted
G-modules and ideals of secant varieties
In the symmetric case the representation is not irreducible.
For instance, consider a $4\times 4$ symmetric matrix $Z^{+}$ with entries $z_{i,j}$. Then $\wedge^{2}Z^{+}$ is given by
$$
\left(\begin{ …
- 8,998