## ＜プレプリント＞Analysis of an algorithm to compute the cohomology groups of coherent sheaves and its applications

作成者 作成者名 所属機関 所属機関名 Graduate School of Mathematics, Kyushu University 九州大学大学院数理学府 英語 Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院 2016-03-22 2016-1 Author's Original open access In algebraic geometry, a number of invariants for classifying algebraic varieties are obtained from the cohomology groups of coherent sheaves. Some typical algorithms to compute the dimensions of the ...cohomology groups have been proposed by Decker and Eisenbud, and their algorithms have been implemented over compute algebra systems such as Macaulay2 and Magma. On the other hand, M. Maruyama showed an alternative method to compute the dimensions in his textbook. However, Maruyama's method was not described in an algorithmic format, and it has not been implemented yet. In this paper, we give an explicit algorithm of his method to compute the dimensions and bases of the cohomology groups of coherent sheaves. We also analyze the complexity of our algorithm, and implemented it over Magma. By our implementation, we examine the computational practicality of our algorithm. Moreover, we give some possible applications of our algorithm in algebraic geometry over fields of positive characteristics.続きを見る

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レコードID 1650651 査読無 Computer algebra Gröbner bases Algebraic geometry Cohomology groups The Global COE Program Mathematics-for-Industry Education & Research Hub グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」 2016.03.30 2018.01.24
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