MODPOSCHAR

Moduli of canonically polarized varieties in positive characteristic

Coordinatore	UNIVERSITY OF CYPRUS    more  Organization address address: KALLIPOLEOS STREET 75 city: NICOSIA postcode: 1678 contact info Titolo: Ms. Nome: Eliza Cognome: Archeou Email: send email Telefono: 35722894076 Fax: 35722894465
Nazionalità Coordinatore	Cyprus [CY]
Totale costo	218˙491 €
EC contributo	218˙491 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2013-IOF
Funding Scheme	MC-IOF
Anno di inizio	2015
Periodo (anno-mese-giorno)	2015-01-05   -   2017-01-04

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITY OF CYPRUS  Organization address address: KALLIPOLEOS STREET 75 city: NICOSIA postcode: 1678 contact info Titolo: Ms. Nome: Eliza Cognome: Archeou Email: send email Telefono: 35722894076 Fax: 35722894465	CY (NICOSIA)	coordinator	218˙491.30

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 Obiettivo del progetto (Objective)

'The main objective of this project is to study the moduli stack of varieties of general type with a fixed Hilbert polynomial defined over a field of positive characteristic. In characteristic zero it is known that it is a separated Deligne-Mumford stack locally of finite type. Moreover, the extended moduli stack of stable varieties is also proper. I would like to investigate to what extend the same properties hold in positive characteristic, if some property fails what is the reason and how the moduli problem could be modified in order to have a separated, proper Deligne-Mumford stack.

The first step will be to consider the case of surfaces. In this case there is resolution of singularities and the semi stable minimal model program works, two properties essential for the construction of a proper moduli stack. In particular, stable surfaces can be defined. In general, the moduli stack of surfaces of general type over a field of positive characteristic is not Deligne-Mumford. This is because there are examples of smooth surfaces of general type with nonreduced automorphism scheme. In order to understand the failure to be Deligne-Mumford the structure of the automorphism scheme of a surface of general type and more generally of a stable surface will be investigated. I would like to find bounds for its length, cases when it is reduced and classify its scheme and group structure. Moreover, all known nonreduced examples suggest that numerical relations exist between the characteristic of the base field and certain invariants of the surface. I would like to investigate if this holds in general. An affirmative answer will allow the construction of Deligne-Mumford substacks of the stack of stable surfaces. Next I will investigate whether the moduli stack is proper. This holds if semistable reduction, or an alternative, holds in positive characteristic.

Depending on progress on the surface case, I will continue my investigation to higher dimensions.'