Algebraic surfaces: from Enriques to Mori
نویسنده
چکیده
Geometry of algebraic surfaces is a classical and beautiful theory. It was developed first by the great Italian geometers. The culmination of their efforts was the Enriques classification of complex projective surfaces. In this talk we outline a possible approach to this classification. Surfaces can be divided into classes according to their Kodaira dimension. Surfaces of negative Kodaira dimension are rational or ruled. Starting points of the classification are theorems of Castelnuovo and Enriques characterizing rational and ruled surfaces, respectively, by their numerical invariants. A surface of nonnegative Kodaira dimension possesses a unique birational minimal model. Those of Kodaira dimension zero are K3, Enriques, Abelian and bielliptic surfaces. Surfaces of positive Kodaira dimension are harder to classify and we only discuss isolated results pertaining to surfaces of general type. If time allows, the extremal ray theory approach to classification is presented. Friday, October 6, 2006 at 2:00 pm Science Center 507
منابع مشابه
Classification of Complex Algebraic Surfaces
In this note we present the classical Enriques’ classification theorem for complex algebraic surfaces. We’ll recall basic facts about the theory of complex surfaces (structure theorems for birational maps), and discuss (using a modern (=Mori) approach) some important results like the Castelnuovo’s rationality criterion and the classification of minimal ruled surfaces. Finally, after the descrip...
متن کاملOn the Topological Classification of Real Enriques Surfaces
This note contains our preliminary calculation of topological types or real Enriques surfaces. We realize 59 topological types of real Enriques surfaces (Theorem 6) and show that all other topological types belong to the list of 21 topological types (Theorem 7). In fact, our calculation contains much more information which is probably useful to constract or prohibit unknown topological types. T...
متن کاملAlgebraic Surfaces in Positive Characteristic
These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-p-geometry, we sketch the Kodaira– Enriques classification. Next, we turn to more special characteristic-p topics, and end by lifting results and applications to characteristic zero. We assume that the reader ...
متن کاملAn Introduction to Complex Algebraic Geometry with Emphasis on the Theory of Surfaces
i Preface These notes are based on courses given in the fall of 1992 at the University of Leiden and in the spring of 1993 at the University of Grenoble. These courses were meant to elucidate the Mori point of view on classification theory of algebraic surfaces as briefly alluded to in [P]. The material presented here consists of a more or less self-contained advanced course in complex algebrai...
متن کاملGrothendieck-riemann-roch and the Moduli of Enriques Surfaces
A (complex) Enriques surface is a projective smooth connected algebraic surface Y over C with H(Y,OY ) = H (Y,OY ) = (0), (Ω 2 Y ) ⊗ 2 ≃ OY but Ω 2 Y 6≃ OY ([CF]). In this note we give a short proof of the fact that the coarse moduli space of complex Enriques surfaces is quasi-affine. This was first shown by Borcherds [B] using the denominator function of a generalized Kac-Moody superalgebra (t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006