Interpolation for Normal Bundles of General Curves (Memoirs of the American Mathematical Society) - Softcover

Atanasov, Atanas; Larson, Eric; Yang, David

Softcover

ISBN 10: 147043489X ISBN 13: 9781470434892

Publisher: Amer Mathematical Society

Synopsis

Given $n$ general points $p1, p2, ldots , pn in mathbb Pr$, it is natural to ask when there exists a curve $C subset mathbb Pr$, of degree $d$ and genus $g$, passing through $p1, p2, ldots , pn$. 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 $NC$ of a general nonspecial curve of degree $d$ and genus $g$ in $mathbb Pr$ (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 $H0(NC(-D)) = 0$ or $H1(NC(-D)) = 0$), with exactly three exceptions.

Edition details

• Publisher: Amer Mathematical Society
• ISBN 10: 147043489X
• ISBN 13: 9781470434892
• Binding: Paperback
• Language: English
• Number of pages: 105