- In mathematics, the
pluricanonical ring of an
algebraic variety V (which is nonsingular), or of a
complex manifold, is the
graded ring R ( V , K ) = R...
-
birationally equivalent. One
useful set of
birational invariants are the
plurigenera. The
canonical bundle of a
smooth variety X of
dimension n
means the...
- {\displaystyle P_{d}=h^{0}(X,K_{X}^{d})=\dim H^{0}(X,K_{X}^{d}).} The
plurigenera are
important birational invariants of an
algebraic variety. In particular...
-
surfaces that are
homeomorphic but have
different plurigenera and
Kodaira dimensions. The
individual plurigenera are not
often used; the most
important thing...
- po****r
subject of
study in the
nineteenth century. Invariants: The
plurigenera are all 1. The
surface is
diffeomorphic to S1×S1×S1×S1 so the fundamental...
- non-singular part of V
extends to a line
bundle on V, and V has the same
plurigenera as any
resolution of its singularities. V has
canonical singularities...
-
plane and the
Hirzebruch surfaces Σr for r = 0 or r ≥ 2. Invariants: The
plurigenera are all 0 and the
fundamental group is trivial.
Hodge diamond: where...
-
primary Kodaira surface by a
group of
order k = 1,2,3,4,6, then the
plurigenera Pn are 1 if n is
divisible by k and 0 otherwise.
Hodge diamond: Examples:...
- non-discrete
algebraic group schemes of
order 2 in
characteristic 2. The
plurigenera Pn are 1 if n is even and 0 if n is odd. The
fundamental group has order...
- the
first invariant pg = P1 of a
sequence of
invariants Pn
called the
plurigenera. In the case of
complex varieties, (the
complex loci of) non-singular...
