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http://www.unimib.it/link/news.jsp?2955028691992140164 regarding the asymptotic properties of linear series, the research will focus on the study of the shape and structure of the Okounkov body and of the volume function; in particular it aims to understand the global conditions on a divisor possessing a rational polyhedral Okounkov body and the relation to the existence of deformations to a toric variety. Regarding cohomological vanishing theorems, the research aims to find new vanishing theorems generalizing the Kawamata-Viehweg one, and to apply them to the estimate of Castelnuovo-Mumford regularity, which controls the complexity of the algebraic equations defining a projective variety, and to the study of the projective normality of adjoint line bundles. It aims to study a multigraded version of Castelnuovo-Mumford regularity, suited to the geometry of toric varieties.
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Early stage researcher or 0-4 yrs (Post graduate), Experienced researcher or 4-10 yrs (Post-Doc)
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