The project is intended to deal with various questions of complex algebraic and analytic geometry, with a special emphasis on effective results and transcendental methods in algebraic geometry. Such methods afford deep insight into spectacular relations between complex analysis, algebraic geometry, topology, and PDE theory. There are two main tools to be employed in the project. On the one hand, LA2 methods, already used byHormander in the study of the Cauchy-Riemann operator, revealed deep links between analytic objects and higher dimensional algebraic geometry, notably Mori's theory. On the other hand, extensive use of the theory turrets, put forth by P. Belong, is intended as a link between multiplier ideal sheaves of Koehler geometry and the Kawamata-Shokurov-Reid technique in higher dimensional algebraic geometry. Effective results in algebraic geometry remain a fertile ground for new research and are likely to increase in importance with the emergence tone areas such as manifolds with special homonymy and Mirror Symmetry. The presence at Warwick otspecialists in such various research fields as algebraic, analytic, Koehler and differential geometry facilitates the interdisciplinary ambitions of the project and makes it likely to succeed.
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