Horrocks-Mumford bundle

Horrocks-Mumford bundle

In algebraic geometry, a branch of mathematics, the Horrocks–Mumford bundleis an indecomposable rank 2 vector bundle on 4-dimensional projective space "P"4 named after Geoffrey Horrocks and David Mumford.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.

ee also

*List of algebraic surfaces

References

*cite journal
author = Horrocks, G.; Mumford, D.
title = A rank 2 vector bundle on "P"4 with 15000 symmetries
journal = Topology
volume = 12
pages = 63–81
year = 1973
doi = 10.1016/0040-9383(73)90022-0
*cite journal
author = Sasakura, Nobuo; Enta, Yoichi; Kagesawa, Masataka
title = Construction of rank two reflexive sheaves with similar properties to the Horrocks–Mumford bundle
journal = Proc. Japan Acad., Ser. A
volume = 69
issue = 5
pages = 144–148
year = 1993


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