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

Atanas Atanasov (author), Eric Larson (author) & David Yang (author)

Softcover

ISBN 10: 147043489X ISBN 13: 9781470434892

Publisher: American Mathematical Society, 2018

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 this title

About the Author

Atanas Atanasov, Harvard University, Cambridge, Massachusetts.

Eric Larson, Stanford University, California.

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• Language: English
• ISBN 10: 147043489X
• ISBN 13: 9781470434892
• Binding: Paperback
• Number of pages: 105