Algebraic Curves and Surfaces: A History of Shapes

Busé, Laurent, Catanese, Fabrizio, Postinghel, Elisa

Algebraic Curves and Surfaces: A History of Shapes
  • 出版商: Springer
  • 出版日期: 2024-05-06
  • 售價: $3,690
  • 貴賓價: 9.5 折 $3,506
  • 語言: 英文
  • 頁數: 205
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031241533
  • ISBN-13: 9783031241536

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This 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 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 such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.

商品描述(中文翻譯)

本書收錄了TiME2019（數學相遇中的寶藏）學校的講義。本書的目的多方面，旨在從不同角度概述代數曲線和曲面（包括高維變量）的廣泛主題：從歷史發展談起，介紹了代數曲面理論以及Castelnuovo和Enriques的代數曲面分類定理；使用像Castelnuovo引入的傳統幾何方法來研究超曲面的線性系統；以及用於找到參數化代數曲線和曲面的隱式方程的代數方法，從傳統的消元理論到涉及syzygy理論和Castelnuovo-Mumford正則性的現代工具。由於我們的主題具有悠久而崇高的歷史，本書無法涵蓋這個廣泛主題的所有細節、理論和應用，但它旨在作為年輕數學家從古典且具有計算視角的角度接觸這一主題的指南，並且對於有經驗的研究人員來說，它是一個有價值的近期應用資源。

作者簡介

Laurent Busé received his PhD degree in Mathematics at the Université of Nice - Sophia Antipolis in 2001 and he is currently a senior researcher at the Inria research center of Université Côte d'Azur. His main research interests focus on computational methods in algebraic geometry and commutative algebra, more specifically on elimination theory, the geometry of algebraic curves and surfaces and their applications in the fields of geometric modeling and geometry processing.

Fabrizio Catanese studied at the Universita' di Pisa and Scuola Normale Superiore 1968-1974, held the Chair of Geometry 1980-1997 in Pisa, the Gauss Chair of Complex Analysis in Goettingen, 1997-2001, then has been professor in Bayreuth since 2001. He is Research Scholar at the Korean Institute for Advanced Study and member of the Accademia Nazionale dei Lincei, the Goettingen Academy, the Academia Europaea. He has been visiting professor at many international Universities and research centres.

Elisa Postinghel received her PhD in Mathematics from the University Roma Tre in 2010. She was a lecturer at Loughborough University between 2016 and 2020 and she is currently a senior researcher at the University of Trento. Her research work is in algebraic geometry; her main interests span classical topics such as polynomial interpolation problems on higher dimensional varieties as well as birational geometry and positivity properties of divisors and curves on Mori dream spaces.

作者簡介(中文翻譯)

Laurent Busé於2001年在尼斯-索菲亞-安蒂波利斯大學獲得數學博士學位，目前是Université Côte d'Azur的Inria研究中心的高級研究員。他的主要研究興趣集中在代數幾何和交換代數的計算方法，特別是消去理論、代數曲線和曲面的幾何以及它們在幾何建模和幾何處理領域的應用。

Fabrizio Catanese在1968年至1974年間就讀於比薩大學和Scuola Normale Superiore，於1980年至1997年在比薩擔任幾何學講座，1997年至2001年在哥廷根擔任複分析高斯講座，自2001年起在拜罗伊特擔任教授。他是韓國高等研究院的研究學者，也是意大利林切學院、哥廷根學院和歐洲科學院的成員。他曾擔任多個國際大學和研究中心的訪問教授。

Elisa Postinghel於2010年從羅馬第三大學獲得數學博士學位。她曾在2016年至2020年間在拉夫堡大學擔任講師，目前是特倫托大學的高級研究員。她的研究工作主要集中在代數幾何領域，主要興趣涵蓋了高維度變量的多項式插值問題，以及Mori夢空間上的有理幾何和曲線的正性性質。

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