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November 2019 A Note on Rational Curves on General Fano Hypersurfaces
Dennis Tseng
Michigan Math. J. 68(4): 755-774 (November 2019). DOI: 10.1307/mmj/1567735281

Abstract

We show that the Kontsevich space of rational curves of degree at most roughly 222n on a general hypersurface XPn of degree n1 is equidimensional of expected dimension and has two components: one consisting generically of smooth embedded rational curves and the other consisting of multiple covers of a line. This proves more cases of a conjecture of Coskun, Harris, and Starr and shows that the Gromov–Witten invariants in these cases are enumerative.

Citation

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Dennis Tseng. "A Note on Rational Curves on General Fano Hypersurfaces." Michigan Math. J. 68 (4) 755 - 774, November 2019. https://doi.org/10.1307/mmj/1567735281

Information

Received: 8 November 2017; Revised: 1 October 2018; Published: November 2019
First available in Project Euclid: 6 September 2019

zbMATH: 07155048
MathSciNet: MR4029628
Digital Object Identifier: 10.1307/mmj/1567735281

Subjects:
Primary: 14H10, 14J45, 14J70

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 4 • November 2019
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