Let us discuss this more general notion, often called a singular Hermitian metric (though perhaps the name possibly singular Hermitian metric is more appropriate).
Assume, moreover, the metric (e^{-varphi }) restricts to (X_o = pi ^{-1}(o)) as a singular Hermitian metric, and moreover, (e^{-varphi }) is locally integrable on (X_o).
If one can regularize a singular Hermitian metric in the right way, then many of the results we have stated, and will state, can be extended to the singular case.
(Paun [43]) Let (pi : X rightarrow {mathbb D}) be a projective holomorphic family, and let (L rightarrow X) be a holomorphic line bundle admitting a singular Hermitian metric (e^{-varphi }) whose curvature current (sqrt{-1}partial bar{partial }varphi ) is non-negative.
(Siu [49]) Let (pi : X rightarrow {mathbb D}) be a projective holomorphic family, and let (L rightarrow X) be a holomorphic line bundle admitting a singular Hermitian metric (e^{-varphi }) whose curvature current (sqrt{-1}partial bar{partial }varphi ) is non-negative.
Assume also that the line bundle (E_Z rightarrow X) associated to the divisor (Z) has a holomorphic section (f_Z) such that (Z = { x in X ; f_Z(x) = 0}), and a singular Hermitian metric (e^{-lambda _Z}), such that begin{aligned} sup _X |f_Z|^2e^{-lambda _Z} = 1.
As far as we assume a non-singular potential ((V(Phi )<infty) for (-infty <Phi le Phi _infty)) and non-<span class="lh lhl">singular metric (q_{00}propto b) for (r>0), the vacuum solution has a singularity at the origin.
Let (L rightarrow X) be a holomorphic line bundle with a possibly singular Hermitian metric (e^{-varphi }) whose singular locus does not lie in (Z), i.e., such that (e^{-varphi }|_{Z}) is a metric for (L|_Z).
The SVD-MDS method performs the dimensional reduction procedure by using a molecular dynamics approach and by initialing the metric space using a singular value decomposition method, resulting in better representation of the similarities and differences in term of information conservation.
After landing at Yahoo!, Decker promoted a singular focus on cash flow, which she highlights during every quarterly conference call as the company's most important financial metric.
It is a singular document.
