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\(H^1\)-Vanishing Theorems

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Singular Algebraic Curves

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Abstract

We describe different approaches to prove \(H^1\)-vanishing for ideal sheaves of zero-dimensional schemes. When looking for appropriate \(H^1\)-vanishing theorems for the problems discussed in Chap. 4, one has to be aware that the types of zero-dimensional schemes to be considered are quite different (cf. Sects. 2.2.1.4 and 2.3.4).

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Authors and Affiliations

  1. Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany

    Gert-Martin Greuel & Christoph Lossen

  2. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Eugenii Shustin

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  1. Gert-Martin Greuel
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  2. Christoph Lossen
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  3. Eugenii Shustin
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Correspondence to Gert-Martin Greuel .

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Greuel, GM., Lossen, C., Shustin, E. (2018). \(H^1\)-Vanishing Theorems. In: Singular Algebraic Curves. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-03350-7_3

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