Preservation of semistability under Fourier–Mukai transforms

Jason Skelton, Ziyu Zhang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)1-31
Number of pages31
JournalGeometriae Dedicata
Early online date26 May 2017
DOIs
Publication statusE-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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