EPSRC Reference: 
EP/X020592/1 
Title: 
The Moduli Space of Foliated Surfaces 
Principal Investigator: 
Cascini, Professor P 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Imperial College London 
Scheme: 
Standard Research  NR1 
Starts: 
11 September 2023 
Ends: 
10 September 2024 
Value (£): 
80,647

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Algebraic geometry distinguishes itself in that families of projective varieties are often naturally parametrised by a single space, called a moduli space. The geometry of this moduli space determines the behaviour of families of all varieties. In particular, the moduli space of curves is one of the most heavily studied varieties in mathematics. Its construction relies on geometric invariant theory, but it turns out that this method does not extend directly to higher dimensions. Instead, the construction of moduli spaces of varieties of general type follows the path laid out by Kollár and ShepherdBarron in the case of surfaces, where the threedimensional Minimal Model Program plays a prominent role.
The aim of this proposal is to use the recent developments in the Minimal Model Program for foliations over a threefold to construct a moduli space which parametrises pairs (X,F) where X is a complex projective surface and F is a foliation on X of general type, i.e. with big canonical divisor, under some natural assumptions on their singularities.

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Summary 

Date Materialised 


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Organisation Website: 
http://www.imperial.ac.uk 