quintic - definitie. Wat is quintic
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Wat (wie) is quintic - definitie

INDECOMPOSABLE RANK 2 VECTOR BUNDLE ON 4-DIMENSIONAL PROJECTIVE SPACE
Horrocks-Mumford quintic; Horrocks-Mumford surface; Horrocks-Mumford bundle

Quintic      
·adj Of the fifth degree or order.
II. Quintic ·noun A quantic of the fifth degree. ·see Quantic.
Quintic threefold         
Quintic 3-fold; Quintic three-fold; 2875 (number); 2875
In mathematics, a quintic threefold is a 3-dimensional hypersurface of degree 5 in 4-dimensional projective space. Non-singular quintic threefolds are Calabi–Yau manifolds.
Barth–Nieto quintic         
Barth-Nieto quintic; Nieto quintic; Barth quintic
In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by that is the Hessian of the Segre cubic.

Wikipedia

Horrocks–Mumford bundle

In algebraic geometry, the Horrocks–Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space P4 introduced by Geoffrey Horrocks and David Mumford (1973). 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 2 F {\displaystyle \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.