Families of hypersurfaces of large degree

TL;DR

This paper demonstrates that for high-degree hypersurfaces in complex projective space, general families do not possess a dominant set of sections, highlighting limitations in their geometric properties.

Contribution

It establishes a new result about the non-existence of dominant sections in large families of high-degree hypersurfaces.

Findings

High-degree hypersurfaces lack dominant sections in general families.

The result applies to complex projective spaces.

Provides insights into the geometry of large degree hypersurfaces.

Abstract

We show that general moving enough families of high enough degree hypersurfaces in a complex projective space do not have a dominant set of sections.