A short proof of a theorem of M. Hashimoto. (English) Zbl 0820.13010
Summary: Recently M. Hashimoto announced that the resolution of determinantal ideals depend on the characteristic of the base field [cf. M. Hashimoto and K. Kurano, Adv. Math. 94, No. 1, 1-66 (1992; Zbl 0777.13009)]. The purpose of this note is to give a short proof of this result. One should stress that even though the method we use is different from Hashimoto’s, his result provided us with the clue where the additional relation exists.
Citations:
Zbl 0777.13009References:
| [1] | Akin, K.; Buchsbaum, D., Characteristic-free representation theory of the general linear group, Adv. in Math., 58, 149-200 (1985) · Zbl 0607.20021 |
| [2] | Akin, K.; Buchsbaum, D.; Weyman, J., Schur functors and Schur complexes, Adv. in Math., 44, 207-278 (1982) · Zbl 0497.15020 |
| [3] | Hashimoto, M., On the Betti numbers of determinantal ideals (1989), preprint |
| [5] | Kempf, G., Linear systems on homogeneous spaces, Ann. of Math., 103, 557-591 (1976) · Zbl 0327.14016 |
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