-
parameterization exists, the
variety is said to be
unirational. Lüroth's
theorem (see below)
implies that
unirational curves are rational. Castelnuovo's theorem...
- Castelnuovo's
theorem also
implies that any
unirational complex surface is rational,
because if a
complex surface is
unirational then its
irregularity and plurigenera...
-
degree 3 in 4-dimensional
projective space.
Cubic threefolds are all
unirational, but
Clemens &
Griffiths (1972) used
intermediate Jacobians to show that...
-
automorphism group is the
group PSL2(11) of
order 660 (Adler 1978). It is
unirational but not a
rational variety.
Gross &
Popescu (2001)
showed that it is...
-
positive characteristic is that a K3
surface may be
unirational.
Michael Artin observed that
every unirational K3
surface over an
algebraically closed field...
- In all of the
previous cases, the
moduli spaces can be
found to be
unirational,
meaning there exists a
dominant rational morphism P n → M g {\displaystyle...
-
variety of
dimension 19.
Shigeru Mukai showed that this
moduli space is
unirational if g ≤ 13 {\displaystyle g\leq 13} or g = 18 , 20 {\displaystyle g=18...
- non-singular
quartic threefolds are irrational,
though some of them are
unirational.
Burkhardt quartic Igusa quartic Iskovskih, V. A.; Manin, Ju. I. (1971)...
- is nonempty, then X is at
least unirational over k, by
Beniamino Segre and János Kollár. For k infinite,
unirationality implies that the set of k-rational...
-
positive characteristic. In particular,
there are
uniruled (and even
unirational)
surfaces of
general type: an
example is the
surface xp+1 + yp+1 + zp+1...
