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The Nef Cone of the Hilbert Scheme of Points on Rational Elliptic Surfaces and the Cone Conjecture

Part of: Cycles and subschemes Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  08 June 2020

John Kopper
John Kopper*
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
*
e-mail: kopper@psu.edu
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Abstract

We compute the nef cone of the Hilbert scheme of points on a general rational elliptic surface. As a consequence of our computation, we show that the Morrison–Kawamata cone conjecture holds for these nef cones.

Keywords

Moduli spaces of sheavesHilbert schemes of pointselliptic surfacescone conjectureklt Calabi–Yau pairs

MSC classification

Primary: 14C05: Parametrization (Chow and Hilbert schemes)
Secondary: 14J27: Elliptic surfaces 14E30: Minimal model program (Mori theory, extremal rays) 14J50: Automorphisms of surfaces and higher-dimensional varieties

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 216 - 227
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

During the preparation of this article, the author was partially supported by NSF RTG grant DMS-1246844.

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