The Beauville-Bogomolov class as a characteristic class
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arXiv
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| Format: | Preprint |
| Publié: |
2011
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| _version_ | 1866914992376250368 |
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| author | Markman, Eyal |
| author_facet | Markman, Eyal |
| contents | Let X be any compact Kahler manifold deformation equivalent to the Hilbert scheme of length n subschemes on a K3 surface, n>1. We construct over XxX a rank 2n-2 reflexive twisted sheaf E, which is locally free away from the diagonal. The characteristic classes of E are invariant under the diagonal action of an index two subgroup of the monodromy group. Given a point x in X, the restriction E_x of E to {x}xX has the following properties.
(1) The characteristic class k_i(E_x) in H^{i,i}(X,Q) can not be expressed as a polynomial in classes of lower degree, if 1<i<(n+1)/2.
(2) The Beauville-Bogomolov class is equal to c_2(TX)+2k_2(E_x). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1105_3223 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | The Beauville-Bogomolov class as a characteristic class Markman, Eyal Algebraic Geometry Let X be any compact Kahler manifold deformation equivalent to the Hilbert scheme of length n subschemes on a K3 surface, n>1. We construct over XxX a rank 2n-2 reflexive twisted sheaf E, which is locally free away from the diagonal. The characteristic classes of E are invariant under the diagonal action of an index two subgroup of the monodromy group. Given a point x in X, the restriction E_x of E to {x}xX has the following properties. (1) The characteristic class k_i(E_x) in H^{i,i}(X,Q) can not be expressed as a polynomial in classes of lower degree, if 1<i<(n+1)/2. (2) The Beauville-Bogomolov class is equal to c_2(TX)+2k_2(E_x). |
| title | The Beauville-Bogomolov class as a characteristic class |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1105.3223 |