Existence of CR sections for high power of semi-positive generalized Sasakian CR line bundles over generalized Sasakian CR manifolds

TL;DR

This paper proves that under certain positivity and geometric conditions, a generalized Sasakian CR line bundle over a compact manifold is big, extending the understanding of CR sections in complex geometry.

Contribution

It establishes the bigness of semi-positive generalized Sasakian CR line bundles under specific positivity and geometric conditions.

Findings

L is big if h^L is positive at some point and conditions Y(0), Y(1) hold everywhere.

Provides criteria for the existence of CR sections for high powers of L.

Extends previous results to a broader class of generalized Sasakian CR manifolds.

Abstract

Let $X$ be a compact generalized Sasakian CR manifold of dimension $2n-1$, $n\geqslant2$, and let $L$ be a generalized Sasakian CR line bundle over $X$ equipped with a rigid semi-positive Hermitian fiber metric $h^L$. In this paper we prove that if $h^L$ is positive at some point of $X$ and conditions Y(0) and Y(1) hold at each point of $X$, then $L$ is big.