In mathematics, the Coble variety is the
moduli space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spac ...
of ordered sets of 6 points in the
projective plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do ...
, and can be represented as a double cover of the projective 4-space branched over the
Igusa quartic In algebraic geometry, the Igusa quartic (also called the Castelnuovo–Richmond quartic ''CR''4 or the Castelnuovo–Richmond–Igusa quartic) is a quartic hypersurface in 4-dimensional projective space, studied by .
It is closely related to the ...
. It is a 4-dimensional
variety
Variety may refer to:
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Films
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* ''Variety'' (1935 film), ...
that was first studied by
Arthur Coble
Arthur Byron Coble (November 3, 1878 – December 8, 1966) was an American mathematician. He did research on finite geometries and the group theory related to them, Cremona transformations associated with the Galois theory of equations, and t ...
.
See also
*
Coble curve In algebraic geometry, a Coble curve is an irreducible degree-6 planar curve with 10 double points (some of them may be infinitely near points).
They were studied by .
See also
* Coble surface
References
*
*{{Citation , last1=Coble , first1=A ...
*
Coble surface
In algebraic geometry, a Coble surface was defined by to be a smooth rational projective surface with empty anti-canonical linear system , −K, and non-empty anti-bicanonical linear system , −2K, . An example of a Coble surface is th ...
*
Coble hypersurface In algebraic geometry, a Coble hypersurface is one of the hypersurfaces associated to the Jacobian variety of a curve
of genus 2 or 3 by Arthur Coble.
There are two similar but different types of Coble hypersurfaces.
*The Kummer variety of the Jac ...
References
*{{Citation , last1=Hunt , first1=Bruce , title=The geometry of some special arithmetic quotients , publisher=
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
Originally founded in 1842 in ...
, location=Berlin, New York , series=Lecture Notes in Mathematics , isbn=978-3-540-61795-2 , doi=10.1007/BFb0094399 , mr=1438547 , year=1996 , volume=1637
Algebraic varieties