REVIEW 3 cited by
Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved or almost nef. Specifically, we show that such a variety $X$, up to a finite quasi-\'etale cover, admits a rationally connected fibration $X \to A$ onto an abelian variety $A$. For the proof, we develop the theory of positivity of coherent sheaves on projective varieties. As applications, we establish some relations between the geometric properties and positivity of tangent sheaves.
Forward citations
Cited by 3 Pith papers
-
Compact K\"ahler manifolds with nef anti-canonical bundle
Every compact Kähler manifold with nef anti-canonical bundle admits a locally trivial fibration over a Calabi-Yau manifold with rationally connected fibers.
-
On compact K\"ahler manifolds with pseudo-effective tangent bundle
Compact Kähler manifolds with pseudo-effective tangent bundle admit a smooth fibration whose base is an étale quotient of a torus and whose fibers are rationally connected.
-
Fundamental groups of compact K\"ahler manifolds with semi-positive holomorphic sectional curvature
A compact Kähler manifold with semi-positive holomorphic sectional curvature is a locally trivial fibration over a finite étale quotient of a torus with rationally connected projective fibers.
Discussion (0). Continue with ORCID to comment.