Fourier-Mukai Transforms of Slope Semistable Sheaves
on Weierstrass Elliptic Surfaces
Wanmin Liu (Uppsala Univ.)
Jason Lo (California State Univ. Northridge)
Thanks to IBS Center for Geometry and Physics in Pohang, South Korea
Liu was supported by IBS-R003-D1
Preprint is available at wanminliu.github.io
MOTIVATION
smooth proj var
bounded derived category of coherent sheaves
stability condition invariant
(Mumford slope, Gieseker, PT, Bridgeland etc)
relation/ symmetry/ modularity
invariant
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QUESTION
elliptic fiberation
with a section
over a smooth base
relative Fourier-Mukai transform
slope stability condition
What is a notion of stability condition
for slope stability condition under
Key Premise: we do NOT fix Chern characters
(Otherwise, lots of work by Bruzzo, Maciocia, Yoshioka and many...)
singular fibers: nodal or cusp
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Limit Bridgeland Stability Condition
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Theorem (L-Lo)
stability stability
semistability semistability
small modification
torsion sheaf
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Weierstrass elliptic surface
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