Global topology of the Hitchin system - GEOM
Global topology of the Hitchin system - GEOM
Global topology of the Hitchin system - GEOM
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
PGLn <strong>Hitchin</strong> <strong>system</strong> over <strong>the</strong> same <strong>Hitchin</strong> base<br />
T ∗ Pic 0 (C) = Pic 0 (C) × H 0 (C, K) is a group; it acts on M d<br />
by (L, ϕ) ˙ (E, φ) ↦→ (L ⊗ E, ϕ + φ)<br />
❀ action <strong>of</strong> Γ = Pic 0 [n] on ˇM d<br />
ˆM d = M d /T ∗ Pic 0 (C) ∼ = χ −1 (A 0 )/ Pic 0 (C) ∼ = ˇM/Γ<br />
ˆM d , <strong>the</strong> PGLn Higgs moduli space, is an orbifold<br />
<strong>the</strong> Γ action is along <strong>the</strong> fibers <strong>of</strong> ˇχ ❀ PGLn <strong>Hitchin</strong> map<br />
ˆχ : ˆM d = ˇM d /Γ → A 0<br />
ˇM d<br />
<br />
<br />
ˇχ <br />
<br />
<br />
ˆχ <br />
A0 will show generic fibers are dual Abelian varieties;<br />
which are complex Lagrangian due to integrable <strong>system</strong><br />
changing complex structure will lead to special Lagrangian<br />
fibrations; and so to SYZ<br />
ˆM e<br />
17 / 39
Change language