Semi-stability of the tangent sheaf of singular varieties

By Henri Guenancia. 2015

51 citations recorded by the source corpus.

The main goal of this paper is to prove the polystability of the logarithmic tangent sheaf $\mathscr T_X(-D)$ of a log canonical pair $(X,D)$ whose canonical bundle $K_X+D$ is ample, generalizing in a significant way a theorem of Enoki. We apply this result and the techniques involved in its proof to get a version of this theorem for stable varieties (the higher dimensional analogue of Deligne-Mumford's stable curves) and to prove the polystability with respect to any polarization of the tangent sheaf of a singular Calabi-Yau variety.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/531e72466092656d8ceb1cd5e57e862caf76f6d5

How researchers see this paper

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In Geometry and Topology

1. Stefan Kebekus
2. T. Peternell
3. D. Greb
4. Behrouz Taji
5. S. Druel
6. Henri Guenancia
7. Carolina Araujo
8. A. Höring

In Mathematical Physics

1. Stefan Kebekus
2. T. Peternell
3. D. Greb
4. Behrouz Taji
5. Henri Guenancia
6. S. Druel

Citations in the corpus

• The Miyaoka-Yau inequality and uniformisation of canonical models (2015, methodology): “Œeory on klt spaces. With these methods at hand, we establish a Q-analogue of the Bogomolov-Gieseker inequality in Section 6. Section 7 applies this, as well as a recent stability result of Guenancia [Gue16], to establish the Q-Miyaoka-Yauinequality, Œeorem 1.1. Œe second main result, Œeorem 1.2, is”