dc.identifier.uri |
http://dx.doi.org/10.15488/10813 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/10891 |
|
dc.contributor.author |
Bloß, Patrick Alexander
|
eng |
dc.date.accessioned |
2021-04-23T12:18:38Z |
|
dc.date.available |
2021-04-23T12:18:38Z |
|
dc.date.issued |
2021 |
|
dc.identifier.citation |
Bloß, Patrick Alexander: The Infinitesimal torelli theorem for irregular varieties. Hannover : Gottfried Wilhelm Leibniz Institut, Diss., 2021, vii, 77 S. DOI: https://doi.org/10.15488/10813 |
eng |
dc.description.abstract |
In this thesis we prove the infinitesimal Torelli theorem for certain classes of irregular
varieties. Given a compact Kähler manifold, the infinitesimal Torelli problem
asks whether the differential of the period map of a Kuranishi family is injective.
Unlike the classical Torelli theorem for curves, there is a negative answer for example
for hyperelliptic curves of genus greater than 2. Nevertheless, the infinitesimal
Torelli theorem holds for many other classes of manifolds. Following Green’s proof
for sufficiently ample hypersurfaces in arbitrary varieties, we prove it for smooth
ample hypersurfaces and more generally complete intersections in general abelian
varieties by reducing it to showing the surjectivity of certain multiplication maps
of vector bundles on the ambient abelian variety. Then we derive numerical conditions
for such multiplication maps to be surjective giving an effective bound on
Green’s result in this particular case. We also investigate the more general case of
irregular varieties with globally generated cotangent bundle which do not embed
into their Albanese varieties. |
eng |
dc.language.iso |
eng |
eng |
dc.publisher |
Hannover : Institutionelles Repositorium der Leibniz Universität Hannover |
|
dc.rights |
CC BY 3.0 DE |
eng |
dc.rights.uri |
http://creativecommons.org/licenses/by/3.0/de/ |
eng |
dc.subject |
infinitesimal Torelli theorem |
eng |
dc.subject |
period map |
eng |
dc.subject |
irregular varieties |
eng |
dc.subject |
abelian varieties |
eng |
dc.subject |
ample divisors |
eng |
dc.subject |
projective normality |
eng |
dc.subject |
infinitesimaler Torelli-Satz |
ger |
dc.subject |
Periodenabbildung |
ger |
dc.subject |
irreguläre Varietäten |
ger |
dc.subject |
abelsche Varietäten |
ger |
dc.subject |
ample Divisoren |
ger |
dc.subject |
projektive Normalität |
ger |
dc.subject.ddc |
510 | Mathematik
|
eng |
dc.title |
The Infinitesimal Torelli Theorem for Irregular Varieties |
eng |
dc.type |
DoctoralThesis |
eng |
dc.type |
Text |
eng |
dcterms.extent |
vii, 77 S. |
|
dc.description.version |
publishedVersion |
eng |
tib.accessRights |
frei zug�nglich |
eng |