Horrocks-Mumford bundle

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In algebraic geometry, a branch of mathematics, the Horrocks-Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space P⁴. 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.

[edit] See also

• List of algebraic surfaces

[edit] References

• Horrocks, G.; Mumford, D. (1973). "A rank 2 vector bundle on P⁴ with 15000 symmetries". Topology 12: 63–81. 

• Sasakura, Nobuo; Enta, Yoichi; Kagesawa, Masataka (1993). "Construction of rank two reflexive sheaves with similar properties to the Horrocks-Mumford bundle". Proc. Japan Acad., Ser. A 69 (5): 144–148.