1.1.1 Frequently used notation1A2835F01724

Symbol

Meaning

Defined in

$\mathrm{PSH}(X,\theta )$, $\theta _ u$

$\theta $-plurisubharmonic functions; $\theta _ u=\theta +\mathrm{dd}^{\mathrm{c}}u$

definition 5.22.1

$u\preceq v$, $u\sim v$

comparison and equality of ordinary singularity types

definition 16.7.1

$\mathcal I(u)$

multiplier ideal sheaf of $u$

definition 6.8.5

$u\preceq _{\mathcal I}v$, $u\sim _{\mathcal I}v$

comparison and equality of multiplier ideals at all weights

section 5.33

$\nu (u,x)$

Lelong number of $u$ at $x$

section 5.34

$P_\theta (f)$, $V_\theta $

envelope below an obstacle $f$; $V_\theta =P_\theta (0)$

section 5.40

$P_\theta [u]$

envelope of the ordinary singularity type; its fixed points are the ordinary models

definition 5.40.4

$P_\theta [u]_{\mathcal I}$

multiplier-ideal envelope

definition 18.4.1

$\mathrm{MA}_\theta (u)$

Monge–Ampère measure of a bounded potential; where a chapter says so, also the extended measure

proposition 5.28.2

$\mathrm{MA}^{\mathrm{ext}}_\theta (u)$

extended non-pluripolar measure, also written $\langle \theta _ u^ n\rangle $

theorem 13.14.3

$\operatorname {Cap}_\omega $

Hermitian capacity

section 5.29

$v_-(\omega )$, $v_+(\omega )$

lower and upper mass of a Hermitian form; bounded mass property

definition 13.14.14

Gauduchon, balanced and pluriclosed metrics

Hermitian forms $\gamma $ with $\mathrm{dd}^{\mathrm{c}}(\gamma ^{n-1})=0$, $\mathrm d(\gamma ^{n-1})=0$ and $\mathrm{dd}^{\mathrm{c}}\gamma =0$, respectively

definition 11.4.1

$\mathcal T_\gamma $, $d_{\gamma ,d}$

Gauduchon trace map and trace metric

subsection 11.31.1

$\underline{\operatorname {vol}}_\theta $, $\overline{\operatorname {vol}}_\theta $

lower and upper volumes of a singularity type

definition 16.28.58

$\mathcal E_{\mathrm{env}}(X,\theta ,\varphi )$

relative envelope class of a reference $\varphi $

definition 16.28.61

$d_\theta $

volume comparison of ordinary models

definition 13.22.1

$b_ h(f)$

subsolution threshold of a density $f$

theorem 15.28.4

$\mathcal D_ h$, $\rho _ h$

space of density roots and root functional

proposition 15.32.5

$\mathcal V_\mu (\theta )$, $\lambda _\mu (\theta )$

Gauduchon variational volume and root volume

definition 12.2.1