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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.

5 votes
0 answers
75 views

Subadditivity of multiplier ideals with a pluriharmonic function

I would like to have a reference for the following two facts (if true): Let $D$ be a nef and big divisor on an algebraic variety $X$ and $h$ a Hermitian metric with minimal singularities on $D$, wr …
Joaquín Moraga's user avatar
3 votes
0 answers
105 views

Restriction of a singular metric with minimal singularities

Let $X $ be a smooth complex algebraic variety and $L $ a pseudo-effective line bundle on $X $, consider $h $ to be a singular Hermitian metric with minimal singularities on $L$ and $|A|$ be the linea …
Joaquín Moraga's user avatar
6 votes
0 answers
559 views

Pseudo-effective divisor which is not nef in any birational model

Let $X$ be a smooth complex projective algebraic variety and let $D$ be a $\mathbb{Q}$-Cartier pseudo-effective divisor on $X$. Lets say that $D$ is birationally nef if there exists a birational ratio …
Joaquín Moraga's user avatar
3 votes
0 answers
142 views

Non-snc locus relative to a smooth morphism

Let $f\colon X\rightarrow Y$ be a smooth morphism between smooth varieties and $B\subset Y$ a simple normal crossing divisor such that $f^*(B)$ is simple normal crossing as well. Consider a semiample …
Joaquín Moraga's user avatar