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Details of Grant 

EPSRC Reference: EP/J019356/1
Title: Foliation Theory in Birational Geometry
Principal Investigator: Cascini, Professor P
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Dept of Mathematics
Organisation: Imperial College London
Scheme: Standard Research
Starts: 28 January 2013 Ends: 27 January 2016 Value (£): 218,570
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
05 Mar 2012 Mathematics Prioritisation Panel Meeting March 2012 Announced
Summary on Grant Application Form
The goal of the Minimal Model Program is to generalise the main results

of the Castelnuovo-Enrique-Severi classification of algebraic surfaces, to

higher dimensional projective varieties.

The programme was started by Mori in the 1980s, for which he won the

prestigious Fields Medal. It was successfully carried out for projective

threefolds by Kawamata, Kollár, Miyaoka, Mori, Reid, Shokurov and many

others. More recently, some of these results were also generalised to any dimension.

The purpose of the proposed research is to develop new techniques, using

Foliation Theory, to solve some of the current obstacles in the Minimal

Model Program. This will be achieved by combining together tools from different areas of mathematics,

such as Number Theory, Kähler Geometry and Analysis. In particular, I plan to use the new results

in the Minimal Model Program to study the classification of foliations over

a projective variety.

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