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Abstract
For a trivial elliptic fibration X=C×SX=C×S with C an elliptic curve and S a projective K3 surface of Picard rank 1, we study how various notions of stability behave under the Fourier–Mukai autoequivalence ΦΦ on Db(X)Db(X), where ΦΦ is induced by the classical Fourier–Mukai autoequivalence on Db(C)Db(C). We show that, under some restrictions on Chern classes, Gieseker semistability on coherent sheaves is preserved under ΦΦ when the polarisation is ‘fiber-like’. Moreover, for more general choices of Chern classes, Gieseker semistability under a ‘fiber-like’ polarisation corresponds to a notion of μ∗μ∗-semistability defined by a ‘slope-like’ function μ∗μ∗.
Original language | English |
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Pages (from-to) | 1-31 |
Number of pages | 31 |
Journal | Geometriae Dedicata |
Early online date | 26 May 2017 |
DOIs | |
Publication status | E-pub ahead of print - 26 May 2017 |
Keywords
- Derived categories
- Elliptic fibrations
- Fourier–Mukai transforms
- Moduli spaces of sheaves and complexes
- Stability conditions
ASJC Scopus subject areas
- Geometry and Topology
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Dive into the research topics of 'Preservation of semistability under Fourier–Mukai transforms'. Together they form a unique fingerprint.Projects
- 1 Finished
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Alastair Craw - Bridgeland Stability and the Moveable Cone
Craw, A. (PI)
Engineering and Physical Sciences Research Council
3/04/13 → 2/10/16
Project: Research council