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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Algebraic Curves: Towards Moduli Spaces

Algebraic Curves: Towards Moduli Spaces

Kazaryan, Maxim E.
Lando, Sergei K.
Prasolov, Victor V.

Hardcover

Series: Moscow Lectures, Book 2

General MathematicsGeometryPhysics

ISBN10: 3030029425
ISBN13: 9783030029425
Publisher: Springer Nature
Published: Feb 6 2019
Pages: 231
Weight: 1.16
Height: 0.63 Width: 6.14 Depth: 9.21
Language: English

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.

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