Objetivo We propose major advances in several fundamental questions of algebraic geometry, centering around the invariants of varieties, that we will attack on two fronts. One direction considers birational invariants and rationality properties. The other studies deformation properties of varieties, especially in terms of curve-counting invariants. Accordingly, we divide the material into three main projects. In the first, we will prove rationality theorems for many new birational quotients obtained via divided powers. The second project sets up a novel method of counting tropical curves, that will lead to results on tropical correspondences. Our third project extends the ideas of the second, proving deep enumerative results in log geometry; we expect this to provide a state-of-the-art enumerative interpretation of the divisor-line bundle equivalence in log tropical terms. The University of Warwick is the ideal venue for this research. The PI will benefit from the extensive experience of Miles Reid and Christian Böhning, world experts in birational geometry and the modern study of rationality questions, and from collaboration with Diane Maclagan, an acknowledged authority in tropical geometry. Ámbito científico natural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programa(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Tema(s) MSCA-IF-2016 - Individual Fellowships Convocatoria de propuestas H2020-MSCA-IF-2016 Consulte otros proyectos de esta convocatoria Régimen de financiación MSCA-IF-EF-ST - Standard EF Coordinador THE UNIVERSITY OF WARWICK Aportación neta de la UEn € 183 454,80 Dirección Kirby Corner Road - University House CV4 8UW Coventry Reino Unido Ver en el mapa Región West Midlands (England) West Midlands Coventry Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 183 454,80
