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Qilin Yang

Publications and source records attributed to Qilin Yang.

4 recordsLinked to original sources
arXiv2015

On Fano threefolds with semi-free ${\mathbb C}^*$-actions, I

Let $X$ be a Fano threefold and $\C ^* \times X\rightarrow X$ an algebraic action. Then $X$ has a $S^1$-invariant Kähler structure and the corresponding $S^1$-action admits an equivariant moment map which is at the same time a perfect Bott-Morse function. We will initiate a program to classify the Fano threefolds with semi-free ${\mathbb C}^*$-actions using Morse theory and the holomorphic Lefschetz fixed point formula as the main tools. In this paper we give a complete list of all possible Fano threefolds without "interior isolated fixed points" for any semi-free ${\mathbb C}^*$-action. For the actions whose fixed point sets have only two connected components, and in a few other cases, we give the realizations of the semi-free $\C^*$-actions.

math.AG↗
arXiv2015

Toric Fano manifolds with nef tangent bundles

In this note we prove that any toric Fano manifold with nef tangent bundle is a product of projective spaces. In particular, it implies that Campana-Peternell conjecture hold for toric manifolds.

math.AG↗
arXiv2014

$L^2$-extension theorems for jet sections of nef holomorphic vector bundles on compact Kähler manifolds and rational homogeneous manifolds, I

In this paper we study holomorphic vector bundles with singular Hermitian metrics whose curvature are Hermitian matrix currents. We obtain an extension theorem for holomorphic jet sections of nef holomorphic vector bundle on compact Kähler manifolds. Using it we prove that Fano manifolds with strong Griffiths nef tangent bundles are rational homogeneous spaces.

math.AG↗