Birational geometry of higher-dimensional Fano varieties of higher index

The aim of the project is to study the birational geometry of certain natural classes of higher-dimensional Fano varieties of higher index, such as non-singular hypersurfaces of low degree in the projective space, in particular, to compute their groups of birational automorphisms, and to describe their structures of Mori fibre spaces. This is an exciting project in an area where the techniques are now well developed and convenient to apply, providing an opportunity for the student to start original research early within the studentship, as well as becoming familiar with higher-dimensional birational geometry, one of the most active areas of the modern Algebraic Geometry. The student will benefit from the expertise of other members of Algebraic Geometry Research Group in Liverpool and will be able to fruitfully interact with other graduate students in the department. In addition to individual supervision, the student will be able to take advantage of a range of masters level modules and research seminars, both within the University of Liverpool and available via the MAGIC consortium, to obtain a broad mathematical education at a high level.

Applications: A strong background in Pure Mathematics is required. Ideally candidates should have a first BSci or Master of Mathematics qualification (or an equivalent). Some knowledge of basic algebraic geometry is very desirable. In the first instance, and for any additional information, please contact Prof. Aleksandr Pukhlikov.

When applying online, please mention the title of the project , the name of the supervisor and the Leverhulme Trust as the source of funding.