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Results tagged with projective-varieties
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user 88133
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
2
votes
Accepted
Secant variety to a zero-dimensional projective variety
I believe this would be a dual arrangement of a star arrangement.
A star arrangement is a union of subspaces defined as follows. Let $H_1,\dotsc,H_d$ be a collection of hyperplanes and fix an integer …
- 6,237
5
votes
Are "transverse" hyperplane sections of nondegenerate irreducible projectice varieties alway...
This is a bit of a folk theorem. Harris (Algebraic Geometry, Proposition 18.10 and Exercise 18.11) states it for general hyperplane sections, but actually proves it for all generically transverse hype …
8
votes
Accepted
Linear spaces secant to Veronese varieties
Here is an answer in terms of power sum decompositions of polynomials. A point $p \in \mathbb{P}^9$ corresponds to a homogeneous polynomial $P$ of degree $3$ in $3$ variable, defining a plane cubic. P …
- 6,237