Fujita hypothesis and birational models in algebraic geometry

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Date

2019

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Publisher

Faculty of Engineering and Natural Sciences

Abstract

The aim of mv research is to study Fujita hypotheses. which states that if is a smooth projektive varvety of dimension n then: (i) Assume that XV. is.a minimal (i.c.. Ay is nef) varvety of general type.(ie., Ky is big == NY > 9). Then the linear system |nvAx| is free for m > n+ 2; (ii) Let A be an ample invertible sheaf on X. Then the linear system |mJvy + (n +1) Al is free. and JnKy + (n+ 2) Al is verv ample on Y, For surfaces Fujita hypotheses was proved by Igor Reider. In my work I generalize result for X not be a sinooth projektive varyety but F-rational. So if Fujita hypotheses is true for a smooth projektive varyety then it is true for more general case F-rational. I use methods of commutative algebra and definition of tight closure.

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Keywords

Fujita hypothesis, algebra, geometry

Citation

Kunanbaev A / Fujita hypothesis and birational models in algebraic geometry / 6M060100 - Department of Mathematics and Natural sciences / 2019

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