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Results tagged with birational-geometry
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user 503398
Birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.
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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 …
- 141
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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 …
- 141
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answer
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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 …
- 141
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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 …
- 141