Construction of negatively curved complete intersections

TL;DR

This paper uses Donaldson-Auroux theory to construct negatively curved complete intersections in complex projective manifolds, including examples with negative holomorphic bisectional curvature and hyperbolic hypersurfaces, advancing understanding of complex hyperbolic geometry.

Contribution

It introduces a method to construct negatively curved complete intersections and provides explicit examples with negative holomorphic bisectional curvature.

Findings

Existence of compact simply connected Kähler manifolds with negative holomorphic bisectional curvature.

Construction of hyperbolic hypersurfaces.

Bounds for Kobayashi hyperbolic metric on these hypersurfaces.

Abstract

Using the Donaldson-Auroux theory, we construct complete intersections in complex projective manifolds, which are negatively curved in various ways. In particular, we prove the existence of compact simply connected Kahler manifolds with negative holomorphic bisectional curvature. We also construct hyperbolic hypersurfaces and we obtain bounds for their Kobayashi hyperbolic metric.