EPSRC logo

Details of Grant 

EPSRC Reference: EP/L018667/1
Title: Birational geometry in positive characteristic
Principal Investigator: Cascini, Professor P
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Dept of Mathematics
Organisation: Imperial College London
Scheme: EPSRC Fellowship
Starts: 01 October 2014 Ends: 30 September 2019 Value (£): 938,733
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
21 Jan 2014 EPSRC Mathematics Interviews - January 2014 Announced
27 Nov 2013 Mathematics Prioritisation Panel Meeting Nov 2013 Announced
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
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Summary
Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:  
Further Information:  
Organisation Website: http://www.imperial.ac.uk