Paper Title:

Gap for geometric canonical height functions

Published on:

17 July 2023

Primary Category:

Algebraic Geometry

Paper Authors:

Yugang Zhang

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Proves gap around 0 for canonical heights of maps on projective spaces

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If height 0 points Zariski dense, map is birationally isotrivial

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As a corollary, geometric Northcott property on projective plane

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Uses intersection theory, Hilbert schemes, cycle spaces

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Does not rely on complex pluripotential theory

Gap around zero for heights of maps on projective spaces

This paper proves two main results: 1) There is a gap around zero for canonical height functions of endomorphisms on projective spaces over function fields. 2) If height zero points are Zariski dense, the map is birationally isotrivial. As a corollary, there is a geometric Northcott property for such maps on the projective plane.

Topology of spaces of maps to projective space

Preimages stabilization for endomorphisms on projective lines

Rationality of Neron-Tate heights on abelian varieties over function fields

Key results on effective cones of Hyperkähler varieties

Partial orders characterize finitely generated kernels of maps to nilpotent groups

Topological rigidity of maps in positive characteristic

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