VirtBir · Virtual Birationality

Virtual Birationality

The main focus of this project concerns the study of enumerative problems in Complex Algebraic Geometry, and in particular curve counting invariants. The long-term objective of the Project was to provide a solid theoretical foundation to several, physics-inspired results in the field, thereby obtaining new effective and geometrically meaningful methods for computing enumerative invariants where the standard techniques fail. The Project has revolved around two main strands: the first line of research (BIR) devoted to the construction of new methods to relate virtual classes of moduli spaces connected by a rational application, and the second (NAT) centered on the exploitation of these methods to find new effective algorithms for computing Gromov-Witten invariants. Additionally, a wide spectrum of Training Activities for the Fellow were set in place, ranging from focused research-level training on a variety of themes relevant for the project (advanced methods in birational geometry, Gromov-Witten Theory, Donaldson-Thomas and Pandharipande-Thomas theory) to additional professional training in the fields of Communication and Presentation Skills, Team Management and Grant-Writing. As stated in Annex I, page 1, “the overall goal of the proposal is for the applicant to obtain a permanent, independent academic position within the EU, leading her own research team”. There has been substantial success on the Research and Training activities carried out by the Fellow under the supervision of the Project. Most of the Research Objectives detailed in Annex I have been accomplished; the rest of them (see in particular RO3 below) turned out to have the necessary flexibility to open new research directions, which are currently being explored. One of the main consequences of the success of the Project has been its crucial contribution to the achievement of the overall professional goals of the proposal stated above, with the Fellow having been awarded a five year Royal Society Dorothy Hodgkin Research Fellowship which will allow her to build her own research group in Imperial College London.

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