Interpolation for Normal Bundles of General Curves - Brossura

Atanasov, Atanas; Larson, Eric; Yang, David

Brossura

ISBN 10: 147043489X ISBN 13: 9781470434892

Casa editrice: Amer Mathematical Society, 2019

Riassunto

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.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2019
• ISBN 10: 147043489X
• ISBN 13: 9781470434892
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 105
• Contatto del produttore: non disponibile