MODPOSCHAR

Moduli of canonically polarized varieties in positive characteristic

 Coordinatore 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

 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

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

varieties    holds    moduli    surface    structure    scheme    construction    stack    separated    stable    surfaces    moreover    automorphism    examples    deligne    nonreduced    proper    mumford    positive   

 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.'

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