Horrocks–Mumford bundle

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

See also

• List of algebraic surfaces

References

• Horrocks, G.; Mumford, D. (1973). "A rank 2 vector bundle on P⁴ with 15000 symmetries". Topology. 12: 63–81.{{cite journal}}: CS1 maint: multiple names: authors list (link)

• 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.{{cite journal}}: CS1 maint: multiple names: authors list (link)