0
votes
0answers
176 views

Does the normalization of a projective morphism determine the line bundle?

Let $X$ be a smooth, complete algebraic variety and suppose I have two projective, birational morphisms $$f:X \to \mathbb{P}^n$$ and $$g:X \to \mathbb{P}^m,$$ such that the image of $f$ is the ...
2
votes
1answer
472 views

Line bundles, linear systems and normalization

One example that I always have in mind is that the plane nodal (or even the plane cuspidal) cubic curve $X$ is obtained by an appropirate 2-dim linear subsystem of $|\mathcal{O} (3)|$ on ...
0
votes
2answers
160 views

Dimensionality of a map — distance

Hello, I am looking for some words to describe what going on here. I'm sure this is not an original thought, so I'd like to read up on more from others who have thought out this topic further. FORMAT ...
7
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1answer
495 views

Normality of a locus of points in projective space

Let $U_{d,n}\subseteq(\mathbb{P}^d)^n$ denote the locus of $n$-distinct points in projective space $\mathbb{P}^d$ that lie on a rational normal curve of degree $d$, and let $V_{d,n}$ denote its ...