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Results tagged with complete-intersection
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user 40297
25
votes
Accepted
Realizing algebraic curves as complete intersections
1) The genus of a complete intersection of multidegree $(d_1,\ldots ,d_{n-1})$ in $\mathbb{P}^n$ is $g=1+\frac{1}{2} d_1\cdot \ldots \cdot d_{n-1}(\sum d_i-n-1)$ (just compute the degree of the canoni …
- 38k
7
votes
Accepted
Isomorphisms of complete intersections
This always holds for $\dim(X)\geq 3$. The point is that in this case the Picard group of $X$ is cyclic, generated by the line bundle $\mathscr{O}_X(1):= \mathscr{O}_{\mathbb{P}^n}(1)_{|X}$; this is …
- 38k