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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

1 vote
0 answers
109 views

About the finite generation of log canonical rings in BCHM

I have posted this question on MSE but haven't received an answer yet. I rephrase it here. Let $(X,B)$ be a klt pair where $K_X+B$ is $\mathbb{R}$-Cartier. Let $\pi:X\rightarrow U$ be a projective mor …
Hobo's user avatar
  • 141
1 vote
1 answer
118 views

About the semi-ampleness for $\mathbb{R}$-divisor

Let $X$ be a normal proper variety and $D$ an $\mathbb{R}$-Cartier divisor on $X$. Then $D$ is called a semi-ample $\mathbb{R}$-divisor if there is a morphism $f:X\rightarrow Y$ and a ample $\mathbb{R …
Hobo's user avatar
  • 141
1 vote
0 answers
112 views

MMP for surfaces over a curve where the geometric generic fiber is a rational curve

I am looking for an explaination or an reference for the following fact: Let $\pi:X\rightarrow Z$ be a contraction from a smooth surface $X$ to a curve $Z$. Assume that the geometric generic fiber of …
Hobo's user avatar
  • 141
1 vote
0 answers
97 views

Coefficients of members in a base-point free linear system

Let $\mathbb{K}\in \{\mathbb{Z},\mathbb{Q},\mathbb{R}\}$ and let $D$ be a base-point free(or ample if it is necessary) $\mathbb{K}$-divisor on a normal projective variety. I have two questions: When …
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  • 141