Slope semistability of Veronese normal bundles
Ray Shang
TL;DR
This paper proves that all Veronese normal bundles are slope semistable and determines their line bundle decomposition when restricted to lines and rational normal curves.
Contribution
It generalizes the classical well-balanced property of rational normal curves to all Veronese normal bundles and explicitly describes their restrictions.
Findings
Veronese normal bundles are slope semistable.
Line bundle decomposition of degree 2 Veronese normal bundles is determined.
Restriction of these bundles to lines and rational normal curves is characterized.
Abstract
A classical fact is that normal bundles of rational normal curves are well-balanced. We generalize this by proving that all Veronese normal bundles are slope semistable. We also determine the line bundle decomposition of the restriction of degree 2 Veronese normal bundles to lines and rational normal curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology