Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Maxim E. Kazaryan"'
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 t
Publikováno v:
Algebraic Curves ISBN: 9783030029425
The introduction of characteristic classes allows one to see many calculations carried out above in a new light and simplify them. Characteristic classes are a universal tool for computing topological characteristics of algebraic varieties, both smoo
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https://doi.org/10.1007/978-3-030-02943-2_17
https://doi.org/10.1007/978-3-030-02943-2_17
Publikováno v:
Algebraic Curves ISBN: 9783030029425
The line bundles over a given complex curve are in a one-to-one correspondence with the linear equivalence classes of divisors on this curve. Such a class has an integer-valued characteristic, the degree. Since divisors consist of points of the curve
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https://doi.org/10.1007/978-3-030-02943-2_12
https://doi.org/10.1007/978-3-030-02943-2_12
Publikováno v:
Algebraic Curves ISBN: 9783030029425
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https://doi.org/10.1007/978-3-030-02943-2_1
https://doi.org/10.1007/978-3-030-02943-2_1
Publikováno v:
Algebraic Curves ISBN: 9783030029425
Constructing moduli spaces is a technically complicated task, involving the analysis of many subtleties. In this chapter, we will discuss, without going into details, one of the possible methods of carrying out such a construction. We will describe t
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https://doi.org/10.1007/978-3-030-02943-2_14
https://doi.org/10.1007/978-3-030-02943-2_14
Publikováno v:
Algebraic Curves ISBN: 9783030029425
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https://doi.org/10.1007/978-3-030-02943-2_16
https://doi.org/10.1007/978-3-030-02943-2_16
Publikováno v:
Algebraic Curves ISBN: 9783030029425
In the first section of this chapter, we give a proof of the Riemann–Roch formula l(D) − l(K − D) = d − g + 1. In the second section, we present a geometric interpretation of the quantities occurring in the Riemann–Roch formula in terms of
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https://doi.org/10.1007/978-3-030-02943-2_10
https://doi.org/10.1007/978-3-030-02943-2_10
Publikováno v:
Algebraic Curves ISBN: 9783030029425
In this chapter, we show how moduli spaces of maps can be applied to compute topological characteristics of various varieties. The notion of a stable map was introduced by Kontsevich. He applied it to solving the classical problem of enumerating rati
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https://doi.org/10.1007/978-3-030-02943-2_18
https://doi.org/10.1007/978-3-030-02943-2_18
Publikováno v:
Algebraic Curves ISBN: 9783030029425
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https://doi.org/10.1007/978-3-030-02943-2_5
https://doi.org/10.1007/978-3-030-02943-2_5
Publikováno v:
Algebraic Curves ISBN: 9783030029425
In Sect. 6.3, we have already discussed what does the moduli space of elliptic (i.e., genus 1) curves look like. This is a rather typical example, which allows one to observe many features common for all moduli spaces. In this chapter, we will study
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https://doi.org/10.1007/978-3-030-02943-2_13
https://doi.org/10.1007/978-3-030-02943-2_13