Algebraisk geometri
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One of the major discoveries of the last two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional …
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities …
The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only …
In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity …
Originally published in 1911 as number thirteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book presents a general survey of the problem of the 27 …
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
This book establishes the moduli theory of stable varieties, giving the optimal approach to understanding families of varieties of general type. Starting from the Deligne–Mumford …
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate …
The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of …
Originally published in 1913 as number fourteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the …