Bibcode
Colombo, Elisabetta; Pietro Pirola, Gian; Tortora, Alfonso
Referencia bibliográfica
eprint arXiv:math/0005283
Advertised on:
5
2000
Número de citas
0
Número de citas referidas
0
Descripción
Let $X$ be a compact Kahler manifold, and let $L$ be a line bundle
on $X.$ Define $I_k(L)$ to be the kernel of the multiplication map $
Sym^k H^0 (L) o H^0 (L^k).$ For all $h leq k,$ we define a map $
ho
: I_k(L) o Hom (H^{p,q} (L^{-h}), H^{p+1,q-1} (L^{k-h})).$ When $L =
K_X$ is the canonical bundle, the map $
ho$ computes a second
fundamental form associated to the deformations of $X.$ If $X=C$ is a
curve, then $
ho$ is a lifting of the Wahl map $I_2(L) o H^0 (L^2
otimes K_C^2).$ We also show how to generalize the construction of
$
ho$ to the cases of harmonic bundles and of couples of vector
bundles.