Interpolation for Normal Bundles of General Curves (Paperback)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Memoirs of the American Mathematical Society
Release date:	December 2018
Authors:	Atanas Atanasov • Eric Larson • David Yang
Dimensions:	254 x 178mm (L x W)
Format:	Paperback
Pages:	105
ISBN-13:	978-1-4704-3489-2
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN:	1-4704-3489-X
Barcode:	9781470434892

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