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Summary: Stable bundles and the first eigenvalue of the
Laplacian
Claudio Arezzo, Alessandro Ghigi, Andrea Loi
Abstract
In this paper we study the first eigenvalue of the Laplacian on a com-
pact manifold using stable bundles and balanced bases. Our main
result is the following: let M be a compact Kšahler manifold of com-
plex dimension n and E a holomorphic vector bundle of rank r over
M. If E is globally generated and its Gieseker point TE is stable, then
for any Kšahler metric g on M
1(M, g)
4 h0
(E)
r(h0(E) - r)
·
c1(E) []n-1
, [M]
(n - 1)! vol(M, [])
,
where = g is the Kšahler form associated to g.
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