The Infinitesimal Torelli Theorem for hypersurfaces in abelian varieties

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Patrick Alexander Bloß

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OriginalspracheEnglisch
Seitenumfang15
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 19 Nov. 2019

Abstract

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. We will prove it for smooth hypersurfaces in simple abelian varieties with sufficiently high self-intersection giving an effective bound on a result by Green in this particular case.

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The Infinitesimal Torelli Theorem for hypersurfaces in abelian varieties. / Bloß, Patrick Alexander.
2019.

Publikation: Arbeitspapier/Preprint › Preprint

Bloß, P. A. (2019). The Infinitesimal Torelli Theorem for hypersurfaces in abelian varieties. Vorabveröffentlichung online.
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N2 - 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. We will prove it for smooth hypersurfaces in simple abelian varieties with sufficiently high self-intersection giving an effective bound on a result by Green in this particular case.

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