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nalimdif SIGNED

Non-Archimedean limits of differential forms, Gromov-Hausdorff limits and essential skeleta

Total Cost €

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EC-Contrib. €

0

Partnership

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 nalimdif project word cloud

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Project "nalimdif" data sheet

The following table provides information about the project.

Coordinator
KATHOLIEKE UNIVERSITEIT LEUVEN 

Organization address
address: OUDE MARKT 13
city: LEUVEN
postcode: 3000
website: www.kuleuven.be

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Belgium [BE]
 Total cost 166˙320 €
 EC max contribution 166˙320 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2018
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2019
 Duration (year-month-day) from 2019-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    KATHOLIEKE UNIVERSITEIT LEUVEN BE (LEUVEN) coordinator 166˙320.00

Map

 Project objective

In the beginning of 2000s Kontsevich and Soibelman have introduced two variants of the SYZ conjecture originating from string theory: a non-Archimeadean one and a differential-geometric one. Both of these conjectures posit existence of a singular affine manifold (the base of the SYZ fibration) that can be obtained either as a subset of the non-Archimedean analytic space associated to a family of complex projective Calabi-Yau varieties with maximally unipotent monodromy, or as a Gromov-Hausdorff limit of fibres of the family with Ricci-flat metric in the polarization class and normalized diameter (the latter was also independently conjectured by Gross, Wilson, and Todorov). Recent years have seen active developments in both of these conjectures through work of de Fernex, Kollár, Mustaţa, Nicaise, Xu, Gross, Tosatti, Zhang and others. Kontsevich and Soibelman have also conjectured that both approaches give the same result, with corresponding singular affine manifolds naturally isomorphic; unfortunately, the existence of such an isomorphism is open as of now.

The aim of this project is to build tools that will allow both to attack the comparison conjecture and to make progress in the understanding of the collapsing Gromov-Hausdorff limits in the odd-dimensional case (hypekähler case having been extensively studied). The proposed approach is based on the theory of differential forms on non-Archimedean analytic spaces due to Chambert-Loir and Ducros. Firstly, a notion of a non-Archimedean limit of a degenerating family of real forms with values in Chambert-Loir-Ducros forms will be defined. Secondly, the metric structure of the collapsing limit will be described in terms of such non-Archimedean limits of Kähler forms. Thirdly, the canonical affine structure on the limit space conjectured to exist in the metric picture will be studied using non-Archimedean methods, assuming a natural statement about the limits of the solutions of Monge-Ampere equations.

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