Interpolation for Brill–Noether curves in \({\mathbb {P}}^4\)

Abstract

We compute the number of general points through which a general Brill–Noether curve in \({\mathbb {P}}^4\) passes. We also prove an analogous theorem when some points are constrained to lie in a transverse hyperplane. As explained in [10], these results play an essential role in the first author’s proof of the Maximal Rank Conjecture [9].

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Acknowledgements

We would like to thank Joe Harris for his guidance, as well as Ravi Vakil, Izzet Coskun, and members of the MIT and Harvard math departments for helpful conversations.

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Correspondence to Isabel Vogt.

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The first author acknowledges the generous support both of the Fannie and John Hertz Foundation, and of the Department of Defense (NDSEG fellowship). The second author acknowledges the generous support of the National Science Foundation Graduate Research Fellowship Program under DGE-1122374.

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Larson, E., Vogt, I. Interpolation for Brill–Noether curves in \({\mathbb {P}}^4\). European Journal of Mathematics (2020). https://doi.org/10.1007/s40879-020-00410-3

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