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Gap around zero for heights of maps on projective spaces

Published on:

17 July 2023

Primary Category:

Algebraic Geometry

Paper Authors:

Yugang Zhang

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Key Details

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

If height 0 points Zariski dense, map is birationally isotrivial

As a corollary, geometric Northcott property on projective plane

Uses intersection theory, Hilbert schemes, cycle spaces

Does not rely on complex pluripotential theory

AI generated summary

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.

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