Interpolation for Normal Bundles of General Curves
- ISBN-10
- 147043489X
- ISBN-13
- 9781470434892
- Category
- Curves, Algebraic
- Pages
- 105
- Language
- English
- Published
- 2019-02-21
- Publisher
- American Mathematical Soc.
- Authors
- David Yang, Eric Larson, Atanas Atanasov
Description
Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,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 Pr (with d≥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.
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