Lefschetz fibrations on adjoint orbits - PMA
Lefschetz fibrations on adjoint orbits - PMA
Lefschetz fibrations on adjoint orbits - PMA
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Amusing c<strong>on</strong>sequence of the classical symmetries<br />
Corollary (Odd Betti numbers are even)<br />
Let X be a compact Kähler manifold. Then b2k+1 ∈ 2Z.<br />
Proof.<br />
The Hodge Diam<strong>on</strong>d ⇒ br (X ) = <br />
⇒ b2k+1 = <br />
p+q=2k+1<br />
h p,q = 2<br />
p+q=r<br />
h p,q<br />
k<br />
h p,2k+1−p .<br />
p=0<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>
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