| 期刊全称 | Algebraic Curves | | 期刊简称 | Towards Moduli Space | | 影响因子2023 | Maxim E. Kazaryan,Sergei K. Lando,Victor V.‘Prasol | | 视频video | | | 发行地址 | Leads a reader to far advanced topics widely used in modern research, using basic tools from the first two years of university studies.From the very beginning, the study of algebraic curves is aimed a | | 学科分类 | Moscow Lectures | | 图书封面 |  | | 影响因子 | .This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well..The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces..Thebook does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass poi | | Pindex | Textbook 2018 |
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发表于 2025-3-21 19:10:04
