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EnglishIt is well known that for a smooth, projective variety X over C the space of the coniveau filtration N^pH^i(X,Q) is contained in the intersection of the space of the Hodge filtration F^pH^i(X,C) with H^i(X,Q). In general this inclusion is strict. We introduce a natural subspace S^{p,i} of F^pH^i(X,C) such that for any integers i,p, N^pH^i(X,Q) is the intersection of S^{ p,i} with H^i(X,Q). The main technical tool is the use of semi-algebraic sets, which are available by the triangulation of complex projective varieties.
| Titolo: | A remark on the generalized Hodge conjecture. |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Abstract: | It is well known that for a smooth, projective variety X over C the space of the coniveau filtration N^pH^i(X,Q) is contained in the intersection of the space of the Hodge filtration F^pH^i(X,C) with H^i(X,Q). In general this inclusion is strict. We introduce a natural subspace S^{p,i} of F^pH^i(X,C) such that for any integers i,p, N^pH^i(X,Q) is the intersection of S^{ p,i} with H^i(X,Q). The main technical tool is the use of semi-algebraic sets, which are available by the triangulation of complex projective varieties. |
| Handle: | http://hdl.handle.net/11368/2773525 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-014-1301-y |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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