Title: Interpolation for Normal Bundles of General Curves (Memoirs of the American Mathematical Society)
Publisher: Amer Mathematical Society (edition )
Language: English
ISBN 10: 147043489X
ISBN 13: 9781470434892
Binding: Paperback
Condition: Very Good

About this title

Synopsis

Given $n$ general points $p_1, p_2, \ldots , p_n \in \mathbb P^r$, it is natural to ask when there exists a curve $C \subset \mathbb P^r$, of degree $d$ and genus $g$, passing through $p_1, p_2, \ldots , p_n$. In this paper, the authors give a complete answer to this question for curves $C$ with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle $N_C$ of a general nonspecial curve of degree $d$ and genus $g$ in $\mathbb P^r$ (with $d \geq g + r$) has the property of interpolation (i.e. that for a general effective divisor $D$ of any degree on $C$, either $H^0(N_C(-D)) = 0$ or $H^1(N_C(-D)) = 0$), with exactly three exceptions.

About the Author

Atanas Atanasov, Harvard University, Cambridge, Massachusetts.

Eric Larson, Stanford University, California.

David Yang, Massachusetts Institute of Technology, Cambridge, Massachusetts.

"About this title" may belong to another edition of this title.

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