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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Horrocks–Mumford bundle ： ウィキペディア英語版 Horrocks–Mumford bundle In algebraic geometry, the Horrocks–Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space ''P''4 introduced by . It is the only such bundle known, although a generalized construction involving Paley graphs produces other rank 2 sheaves (Sasukara et al. 1993). The zero sets of sections of the Horrocks–Mumford bundle are abelian surfaces of degree 10, called Horrocks–Mumford surfaces. By computing Chern classes one sees that the second exterior power $\backslash wedge^2\; F$ of the Horrocks–Mumford bundle ''F'' is the line bundle ''O(5)'' on ''P4''. Therefore the zero set ''V'' of a general section of this bundle is a quintic threefold called a Horrocks–Mumford quintic. Such a ''V'' has exactly 100 nodes; there exists a small resolution ''V′'' which is a Calabi–Yau threefold fibered by Horrocks–Mumford surfaces. ==See also== *List of algebraic surfaces 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Horrocks–Mumford bundle」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.