Positivity and Vanishing Theorems

Show simple item record Griffiths, Phillip 2020-01-03T15:55:55Z 2020-01-03T15:55:55Z
dc.description Lectures given at the University of Miami, Spring 2020 en_US
dc.description.abstract Existence theorems are a central part of algebraic geometry. These results frequently involve linear problems where positivity assumptions are used to prove existence of solutions by establishing the vanishing of obstructions to that existence. Beginning with Riemann (algebraic curves), Picard (algebraic surfaces) and continuing into more recent times (Lefschetz, Hodge, Kodaira-Spencer and many others since this work) it has come to be understood that the vanishing theorems are intimatedly related to the topology of algebraic varieties. What remains is the case that although the results are about algebraic varieties, analytic tools are needed to establish them. Moreover the property of positivity also appears in other aspects where analytic methods are needed, an example being the proof of the Iitaka conjecture which is central in the classification of algebraic varieties. The purpose of these lectures is to present, sometimes from an historical perspective, some of the principal aspects of the theory. en_US
dc.language.iso en_US en_US
dc.subject algebraic geometry en_US
dc.subject existence theorems en_US
dc.title Positivity and Vanishing Theorems en_US
dc.title.alternative Lectures given at the University of Miami, Spring 2020 en_US
dc.type Lecture/speech en_US

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