dc.identifier.uri |
http://dx.doi.org/10.15488/9921 |
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dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/9979 |
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dc.contributor.author |
Heckel, Tobias
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dc.date.accessioned |
2020-07-08T07:00:24Z |
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dc.date.available |
2020-07-08T07:00:24Z |
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dc.date.issued |
2020 |
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dc.identifier.citation |
Heckel, Tobias: Fano schemes of lines on singular cubic hypersurfaces and their Picard schemes. Hannover : Gottfried Wilhelm Leibniz Universität, Diss., 2020, 98 S. DOI: https://doi.org/10.15488/9921 |
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dc.description.abstract |
To every cubic hypersurface $X$ we associate the parameter space of lines contained in $X$; this is called the Fano scheme of lines on $X$ and denoted $F(X)$. If X admits an isolated singular point of ADE-type, we prove that $F(X)$ admits hypersurface singularities of the same type transversally along the regular part of its singular locus. As was shown by H. Clemens and P. Griffiths, the Albanese variety $\operatorname{Alb}(F(X))$ of the Fano scheme of lines $F(X)$ on a smooth cubic threefold $X$ is isomorphic to the intermediate Jacobian $IJ(X)$ of $X$. G. van der Geer and A. Kouvidakis generalised this result to nodal cubic threefolds, replacing the Albanese variety $\operatorname{Alb}(F(X))$ by the Picard scheme $\operatorname{Pic}^0(F(X))$.
We study more generally degenerations of the Picard scheme $\operatorname{Pic}^0(F(X))$ when the smooth cubic threefold $X$ degenerates to a cubic threefold with unique singular point of type $A_k$ and prove that these degenerations define points in Mumford’s partial compactification $\mathcal{A}_5'$ of the moduli space $\mathcal{A}_5$ of principally polarised Abelian varieties of genus five. |
eng |
dc.language.iso |
eng |
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dc.publisher |
Hannover : Institutionelles Repositorium der Leibniz Universität Hannover |
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dc.rights |
CC BY 3.0 DE |
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dc.rights.uri |
http://creativecommons.org/licenses/by/3.0/de/ |
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dc.subject |
Fano scheme of lines |
eng |
dc.subject |
Cubic hypersurfaces |
eng |
dc.subject |
Picard scheme |
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dc.subject |
Hilbert scheme |
eng |
dc.subject |
ADE singularities |
eng |
dc.subject |
Kubische Hyperflächen |
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dc.subject |
Fano schema der Geraden |
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dc.subject |
Picardschema |
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dc.subject |
Hilbertschema |
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dc.subject |
ADE Singularitäten |
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dc.subject.ddc |
510 | Mathematik
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dc.title |
Fano schemes of lines on singular cubic hypersurfaces and their Picard schemes |
eng |
dc.type |
DoctoralThesis |
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dc.type |
Text |
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dcterms.extent |
98 S. |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
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