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Τι (ποιος) είναι quintic surface - ορισμός

INDECOMPOSABLE RANK 2 VECTOR BUNDLE ON 4-DIMENSIONAL PROJECTIVE SPACE

Horrocks-Mumford quintic; Horrocks-Mumford surface; Horrocks-Mumford bundle

Surface finish

SMALL, LOCAL DEVIATIONS OF A SURFACE FROM A PERFECTLY FLAT IDEAL; DEFINED BY THE THREE CHARACTERISTICS OF LAY, SURFACE ROUGHNESS, AND WAVINESS

Surface texture symbol; Surface texture; Surface topography

Surface finish, also known as surface texture or surface topography, is the nature of a surface as defined by the three characteristics of lay, surface roughness, and waviness.. It comprises the small, local deviations of a surface from the perfectly flat ideal (a true plane).

https://en.wikipedia.org/wiki/Surface_finish

Parametric surface

SURFACE IN THE EUCLIDEAN SPACE

Parametrized surface; Parametrised surface; Parametrized Surface; Surface parameterisation; Parametric object

A parametric surface is a surface in the Euclidean space \R^3 which is defined by a parametric equation with two parameters Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence theorem, are frequently given in a parametric form.

https://en.wikipedia.org/wiki/Parametric_surface

Planetary surface

WHERE THE SOLID (OR LIQUID) MATERIAL OF THE OUTER CRUST ON CERTAIN TYPES OF ASTRONOMICAL OBJECTS CONTACTS THE ATMOSPHERE OR OUTER SPACE

Planet surface; Surface (astronomy); Surfacism; Surface chauvinism

A planetary surface is where the solid or liquid material of certain types of astronomical objects contacts the atmosphere or outer space. Planetary surfaces are found on solid objects of planetary mass, including terrestrial planets (including Earth), dwarf planets, natural satellites, planetesimals and many other small Solar System bodies (SSSBs).

https://en.wikipedia.org/wiki/Planetary_surface

Βικιπαίδεια

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 $\wedge ^{2}F$ 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.

https://en.wikipedia.org/wiki/Horrocks–Mumford bundle