Lefschetz fibrations on adjoint orbits - PMA
Lefschetz fibrations on adjoint orbits - PMA
Lefschetz fibrations on adjoint orbits - PMA
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Basic Hodge Theory<br />
Theorem (Hodge Decompositi<strong>on</strong> Theorem)<br />
Let X be a compact Kähler manifold of dimensi<strong>on</strong> n. Then there<br />
exists a decompositi<strong>on</strong><br />
H k (X , C) = <br />
H p,q (X )<br />
Classical Symmetries:<br />
p+q=k<br />
1. C<strong>on</strong>jugati<strong>on</strong> H p,q (X ) ∼ = H q,p (X )<br />
2. Hodge ⋆−operator H p,q (X ) ∼ = H n−q,n−p (X )<br />
3. Serre duality H p,q (X ) ∼ = H n−p,n−q (X )<br />
Elizabeth Gasparim <str<strong>on</strong>g>Lefschetz</str<strong>on</strong>g> <str<strong>on</strong>g>fibrati<strong>on</strong>s</str<strong>on</strong>g> <strong>on</strong> <strong>adjoint</strong> <strong>orbits</strong>