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Birational Geometry Of Algebraic Varieties Pdf Free

 
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Librarians Authors Publishing partners Agents Corporates Additional Information Accessibility Our blog News Contact us Help Cambridge Core terms of use Feedback Site map Join us online Legal Information Rights & Permissions Copyright Privacy Policy Terms of use Cookies Policy Cambridge University Press 2016 Back to top Cambridge University Press 2016 Back to top . A uniruled variety does not have a minimal model, but there is a good substitute: Birkar, Cascini, Hacon, and McKernan showed that every uniruled variety over a field of characteristic zero is birational to a Fano fiber space.[3] This leads to the problem of the birational classification of Fano fiber spaces and (as the most interesting special case) Fano varieties. You are using a web browser we do not support. Algebraic varieties differ widely in how many birational automorphisms they have. That being said, the minimal model conjecture would imply that every variety X is either covered by rational curves or birational to a minimal variety Y. (1971), "Three-dimensional quartics and counterexamples to the Lroth problem", Matematicheskii Sbornik, Novaya Seriya, 86: 140166, doi:10.1070/SM1971v015n01ABEH001536, MR0291172 Kollr, Jnos; Mori, Shigefumi (1998), Birational Geometry of Algebraic Varieties, Cambridge University Press, ISBN0-521-63277-3, MR1658959 Mori, Shigefumi (1988), "Flip theorem and the existence of minimal models for 3-folds", Journal of the American Mathematical Society, American Mathematical Society, 1 (1): 117253, doi:10.2307/1990969, ISSN0894-0347, MR924704 . A projective variety X is called minimal if the canonical bundle KX is nef. together with the group PGL(3,C) of automorphisms of P2, by Max Noether and Castelnuovo. In dimension 2, every Fano variety (known as a Del Pezzo surface) over an algebraically closed field is rational.

Close this message to accept cookies or find out how to manage your cookie settings. Minimal models in higher dimensions[edit]. At first, it is not clear how to show that there are any algebraic varieties which are not rational. Cancel Log in . We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Minimal models and resolution of singularities[edit]. < Back to search results HomeRedirect support . When it exists, Y is called a minimal model of X. Then a birational map from X to the projective space Pn of lines through p is given by sending a point q in X to the line through p and q.

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