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Hodge-Gaussian maps | | Elisabetta Colombo
; Gian Pietro Pirola
; Alfonso Tortora
; | | Date: |
30 May 2000 | | Subject: | Algebraic Geometry MSC-class: 14C30; 14H15 | math.AG | | Affiliation: | Dipartimento di Matematica, Universita di Milano), Gian Pietro Pirola (Dipartimento di Matematica, Universita di Pavia), Alfonso Tortora (Dipartimento di Matematica, Universita di Milano | | Abstract: | Let $X$ be a compact Kähler 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. | | Source: | arXiv, math.AG/0005283 | | Services: | Forum | Review | PDF | Favorites | |
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