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.
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2013-IOF
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
1678 Nicosia
Cyprus
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.