Book Review: Methods of algebraic geometry. Vol. III. Birational geometry
نویسندگان
چکیده
منابع مشابه
Exercises in the Birational Geometry of Algebraic Varieties
The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary. However, the main parts, Chapters 1–3 and 5, still form the foundations of the subject. These note...
متن کاملBirational geometry of quadrics
A central method in the theory of quadratic forms is the study of function fields of projective quadrics. In particular, it is important to ask when there is a rational map from one quadric over a field to another. This suggests the problem of determining when two quadrics are birational, which turns out to be much harder. The answer is known for quadratic forms of dimension at most 7 (thus for...
متن کاملBirational geometry of defective varieties
Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness, rational connectivity, and rationality. AMS Subject Classification: 14N05.
متن کاملCohomological Methods in Algebraic Geometry
We begin this paper with a discussion of n-dimensional algebraic Vector bundles. Vector bundles of rank n may be identified with locally free Ox-modules of rank n. Several sections are dedicated to reviewing the basic notions of scheme-theory. We show how to construct the projectization of arbitrary rings. This construction corresponds to the construction of the tautological line bundle over an...
متن کاملTopological Methods in Algebraic Geometry
Preface These are live-texed lecture notes for a course taught in Cambridge during Michaelmas 2013 by Burt Totaro, on a hodgepodge of topics at the intersection of algebraic topology and algebraic geometry. An unfortunate side effect of live-texing is that it tends to introduce a lot of errors, which are solely the fault of the scribe. If you find any, please let me know at
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1955
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1955-09910-5