Questions tagged [complete-intersection]
The complete-intersection tag has no usage guidance.
4
questions
13
votes
1
answer
2k
views
Realizing algebraic curves as complete intersections
I have two related questions about smooth complete algebraic curves (over $\mathbb{C}$).
Does there exist a smooth complete algebraic curve $X$ that cannot be embedded as a complete intersection in $\...
11
votes
1
answer
2k
views
geometric interpretation and differences of Gorenstein rings, Complete intersections and regular rings
Let $R$ be a local Noetherian ring.
What is the geometric interpretation of:
1- Gorenstein rings
2- Complete intersections
3- Regular rings?
and how can I realize differences by geometric ...
4
votes
2
answers
262
views
When is a pair of space curves that intersect (plenty) a complete intersection?
Let there be two curves of degree $d=2 m^2$ in $\mathbb{A}^3$ having $\geq c d^2$ points of intersection, where $c>0$ is a constant. Then their union $V$ is a curve of degree $2 d = 4 m^2$. Can $V$ ...
4
votes
0
answers
684
views
Factoriality of complete intersections
Let $X\subset\mathbb{P} _{\mathbb{C}}^N$ be a normal complete intersection.
$X$ is called factorial if every Weil divisor on it is Cartier;
equivalently if all local rings $\mathcal{O}_{X,x}$ are ...