Semistable sheaves in positive characteristic

By A. Langer. 2004

364 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82638bb53cc6c253982fc981b237d97c702c14d3

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stability conditions on Kuznetsov components (2017, positive): “To this end, as in [Lan04], we consider the following version of Theorem 8.”
On the S-fundamental group scheme (2009, background): “We should note that a strong version of boundedness of semist able sheaves (see [26] and [28]) is frequently used in proofs in this paper (although we could do without it in many but not all places).”
Stability conditions and extremal contractions (2012, neutral): “([8], [16], [23]) Let X be a smooth projective variety of dimX = d ≥ 2, and H1, · · · , Hd−1 nef divisors on X such that the 1-cycle H1 · · ·Hd−1 is numerically nontrivial.”
Bogomolov’s inequality for Higgs sheaves in positive characteristic (2015, methodology): “First we use the results of [21] to prove a weak version of Bogomolov’s inequality for vector bundles with generalized connections (see Theorem 6).”
Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups (2013, background): “Besides the intimate relation with the representation of π1, the notion of strongly semistability is also useful in other situation, for example, in Langer’s proof of boundedness of semistable sheaves and Bogomolov’s inequality in positive characteristic [17].”
A decomposition theorem for singular spaces with trivial canonical class of dimension at most five (2016, background): “By [Lan04, Corollary 5.4], the sheaves E i / E i − 1 | C and Ω 1 X | C are semistable.”
Fourier-Mukai partners of K3 surfaces in positive characteristic (2011, background): “ [H2, Section 10.3], with a more comprehensive treatment in [HL] and some additional non-emptiness results in [M]. For a discussion of semistable sheaves in positive characteristic see Langer’s paper [Lan]. If we ﬁx a vector v ∈ A∗(X) num,Q, we then get an open and closed substack Mh(v) ⊂ Mh classif”
Moduli of twisted sheaves (2004, methodology): “Following Langer [41], we choose a nef divisor A on Y such that TY (A) is globally generated, and we set”
Looking out for stable syzygy bundles (2003, background): “Then the syzygy bundle of the family of all monomials ∈ K[X0, . . . , XN ] of fixed degree d is semistable.”
Rationally connected foliations after Bogomolov and McQuillan (2005, methodology): “We refer to [Fle84] and [ Lan04 ] for a discussion and an explicit bound for the mi.”
Lectures on Bridgeland Stability (2016, background): “2] or [Lan04]): up to replacing H with a multiple uH, for u≫ 0 fixed, there exists a smooth projective curve C ∈ |H| such that E|C is again slope semistable.”