Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tilt-stability, vanishing theorems and Bogomolov-Gieseker type
  inequalities   We investigate the tilt-stability of stable sheaves on projective varieties
with respect to certain tilt-stability conditions depends on two parameters
constructed by Bridgeland. For a stable sheaf, we give effective bounds of
these parameters such that the stable sheaf is tilt-stable. These allow us to
prove new vanishing theorems for stable sheaves and an effective Serre
vanishing theorem for torsion free sheaves. Using these results, we also prove
Bogomolov-Gieseker type inequalities for the third Chern character of a stable
sheaf on $\mathbb{P}^3$.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg