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

Algebra

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About the Author Atanas Atanasov, Harvard University, Cambridge, Massachusetts.Eric Larson, Stanford University, California.David Yang, Massachusetts Institute of Technology, Cambridge, Massachusetts. Product Description 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.

Product Specifications

Format: Paperback
ASIN: 147043489X
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 December 2018
Listed Since: 25 September 2018

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

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