Titlebook: Algebraic Curves and Surfaces; A History of Shapes Laurent Busé,Fabrizio Catanese,Elisa Postinghel Book 2023 The Editor(s) (if applicable)

摘要

The ,-Theorem: The Classification of Surfaces and Its Historical Development,century, and relies on two main results: .We shall especially carefully explain the latter theorem, whose analogue for higher dimensional varieties is still conjectural, and is called the abundance conjecture, crucial for the extension of the Castelnuovo-Enriques classification to higher dimensions.

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慎重

Implicit Representations of Rational Curves and Surfaces,r surface parametrization. This is an old and classical problem in elimination theory that has seen a renewed interest during the last thirty years because of its usefulness in geometric modeling: rational curves and surfaces are widely used for defining 3D shapes and implicitization provides method

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Book 2023overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of suc

背书

The ,-Theorem: The Classification of Surfaces and Its Historical Development,.A special role plays what we call the Crucial Theorem, on the characterization of the non-ruled minimal surfaces with vanishing Chern numbers as complex tori or surfaces isogenous to an elliptic product. This characterization was not fully achieved by Enriques, and we discuss in the appendix the cases that he was missing.

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慢跑

2524-857X ebraic surfaces is given with full treatment of the P_{12}-tThis volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimen

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样式

Implicit Representations of Rational Curves and Surfaces,ebra have been used to tackle the implicitization problem, from the classical Sylvester resultant and Hilbert-Burch theorem, to the more recent approaches that are based on the study of syzygy modules and certain blowup algebras associated to rational maps.