Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture

Arend Bayer; Aaron Bertram; Emanuele Macri; Yukinobu Toda

doi:10.1090/S1056-3911-2014-00637-8

Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture

Arend Bayer
, Aaron Bertram
, Emanuele Macri
, Yukinobu Toda

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that K_X + 6L is very ample when L is ample, and that 5L is very ample when K_X is trivial.

Original language	English
Pages (from-to)	693-710
Number of pages	17
Journal	Journal of Algebraic Geometry
Volume	23
Early online date	28 Jan 2014
DOIs	https://doi.org/10.1090/S1056-3911-2014-00637-8
Publication status	Published - 31 Oct 2014

Keywords / Materials (for Non-textual outputs)

Bogomolov-Gieseker inequality
Bridgeland stability conditions
Derived category
adjoint line bundles
Fujita conjecture

Access to Document

10.1090/S1056-3911-2014-00637-8

REF-fujitaAccepted author manuscript, 295 KB

http://uk.arxiv.org/abs/1106.3430

Cite this

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title = "Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture",

abstract = "We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that K\_X + 6L is very ample when L is ample, and that 5L is very ample when K\_X is trivial.",

keywords = "Bogomolov-Gieseker inequality , Bridgeland stability conditions, Derived category, adjoint line bundles, Fujita conjecture",

author = "Arend Bayer and Aaron Bertram and Emanuele Macri and Yukinobu Toda",

note = "17 pages. v2: exposition improved based on referee's comments. To appear in Journal of Algebraic Geometry",

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T1 - Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture

AU - Bayer, Arend

AU - Bertram, Aaron

AU - Macri, Emanuele

AU - Toda, Yukinobu

N1 - 17 pages. v2: exposition improved based on referee's comments. To appear in Journal of Algebraic Geometry

PY - 2014/10/31

Y1 - 2014/10/31

N2 - We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that K_X + 6L is very ample when L is ample, and that 5L is very ample when K_X is trivial.

AB - We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that K_X + 6L is very ample when L is ample, and that 5L is very ample when K_X is trivial.

KW - Bogomolov-Gieseker inequality

KW - Bridgeland stability conditions

KW - Derived category

KW - adjoint line bundles

KW - Fujita conjecture

U2 - 10.1090/S1056-3911-2014-00637-8

DO - 10.1090/S1056-3911-2014-00637-8

M3 - Article

SN - 1056-3911

VL - 23

SP - 693

EP - 710

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

ER -

Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture

Abstract

Keywords / Materials (for Non-textual outputs)

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