EPSRC Reference: 
EP/L018667/1 
Title: 
Birational geometry in positive characteristic 
Principal Investigator: 
Cascini, Professor P 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Imperial College London 
Scheme: 
EPSRC Fellowship 
Starts: 
01 October 2014 
Ends: 
30 September 2019 
Value (£): 
938,733

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Algebraic geometry is the study of algebraic varieties, i.e. the sets of
solutions of a collection of polynomial equations. Even though algebraic
geometry started more than two thousand years ago, with the study of
the geometry of conic sections, such as circles, we still cannot completely
answer many simple and fundamental questions. For example, given a
collection of polynomials, with finitely many solutions, we would like to
know the number of these solutions. We know this number in many special
cases, and these cases have interesting applications in many different fields,
such as engineering and biology.
The goal of the Minimal Model Programme, started by Fields medalist
S. Mori in the 1980s, is to generalise the main results of the classification
of algebraic surfaces, due to Castelnuovo, Enrique and Severi, to higher
dimensional projective varieties. In particular, it predicts the existence
of a birational model for any complex projective variety which is as simple
as possible. The last decade has seen exceptional activity towards
Mori's programme, and it is very reasonable to expect that much more
progress will be made in the near future.
The aim of this proposal is to study new methods, by combining tools in
commutative algebra and birational geometry, which would improve these
results and solve some of the main open problems in the Minimal Model
Programme over any algebraically closed field.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

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