Movable curves and semistable sheaves

By D. Greb, Stefan Kebekus, T. Peternell. 2014

78 citations recorded by the source corpus.

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on singular varieties, as well as a characterisation of finite quotients of Abelian varieties via a Chern class condition.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9ee0df2a68537bca2a42f61b8430f437159a946e

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The Miyaoka-Yau inequality and uniformisation of canonical models (2015, result): “enumericalcurve class, cf. [GKP15, Def. 2.2]. If X is Q-factorial, our deﬁnition of slope agrees with that of [GKP15, Def. 2.10]. The standard proofs of the following elementary facts carry over from [GKP15] essentially verbatim. Lemma 2.22 (Elementary properties of slope). In the setup of Deﬁnition”
Foliations with positive slopes and birational stability of orbifold cotangent bundles (2015, background): “ by the ﬁrst named author together with T. Peternell in [12]. These results will play a crucial role in the proof of our algebraicity criteria, cf. section four. One can proﬁtably consult the article [18], where the interested reader will ﬁnd a detailed presentation together with a “singular version”
Algebraic integrability of foliations with numerically trivial canonical bundle (2017, background): “y ﬂat. - Strictly speaking, both statements are established so far only when X is smooth. However, it is not diﬃcult to derive the assertions in the normal case by passing to a desingularisation; see [GKP16b] for the techniques. 2.7. Deﬁnition. Let X be a normal projective variety of dimension n tha”
Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups (2017, background): “the holonomy representation in case where TX is stable only with respect to a movable curve class, or with respect to nef divisors. Stability with respect to a movable class is discussed in the paper [GKP16a]. We refer to [GKP16a, Def. 2.11]for a precise deﬁnition. Corollary6.9(Stabilityandirreducib”