Canonical currents and heights for K3 surfaces

Simion Filip, Valentino Tosatti

Type: Article

Publication Date: 2023-01-01

Citations: 5

DOI: https://doi.org/10.4310/cjm.2023.v11.n3.a2

Abstract

We construct canonical positive currents and heights on the boundary of the ample cone of a K3 surface.These are equivariant for the automorphism group and fit together into a continuous family, defined over an enlarged boundary of the ample cone.Along the way, we construct preferred representatives for certain height functions and currents on elliptically fibered surfaces.

Locations

Cambridge Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (65)

Action	Title	Year	Authors
+	Notions of Convexity	2007	Lars Hörmander
+	Variation of the Canonical Height On Elliptic-Surfaces II:	1994	Joseph H. Silverman
+ PDF Chat	Large Complex Structure Limits of K3 Surfaces	2000	Mark Gross P. Μ. H. Wilson
+ PDF Chat	Lectures on the Mordell-Weil Theorem	1989	Jean-Pierre Serre
+	Algebraic geometry and arithmetic curves	2003	Qing Liu
+	Algebraic Structures of Symmetric Domains	1981	Ichirō Satake
+	Ergodic Theory and Semisimple Groups	1984	Robert J. Zimmer
+	Advanced Topics in the Arithmetic of Elliptic Curves	1994	Joseph H. Silverman
+ PDF Chat	Degeneration of algebraic manifolds and the spectrum of Laplacian	1997	Kenichi Yoshikawa
+ PDF Chat	Sur la laminarité de certains courants	2004	H DETHELIN