Questions tagged [complete-intersection]

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13 votes
1 answer
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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 $\...
Robin's user avatar
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11 votes
1 answer
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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 ...
user 1's user avatar
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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 $V$ ...
H A Helfgott's user avatar
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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 ...
gio's user avatar
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