# Existence of embeddings of varieties in projective spaces whose points are spanned by low degree smoothable zero-dimensional subschemes

Keywords:
embeddings of projective varieties, zero-dimensional scheme

### Abstract

Let *X* be an integral projective variety. Set *n:=* dim *X*. Let *e(X) ≥ 2n+1* be the embedding dimension of *X* (we may take *e(X)=2n+1* if *X* is smooth). Fix integers *δ* and *r ≥ e(X)*. We prove the existence of many embeddings *j:**X↪ P^{r}*such that deg

*(X) ≥ δ*and every point of

*is spanned by a low degree smoothable zero-dimensional subscheme of*

**P**^{r}*X*.

Published

2020-03-28

How to Cite

*Gulf Journal of Mathematics*,

*8*(1), 1-5. Retrieved from https://gjom.org/index.php/gjom/article/view/281

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Section

Articles