20.1.1 The notion of b-divisors`2C74B684280C`

The b-divisors defined in this section are sometimes called b-divisor classes. We always omit the word classes to save space.

Let $X$ be a connected compact Kähler manifold of dimension $n$.

Let us recall the following elementary result regarding how cohomology behaves under blow-up.

Proposition 20.1.2.7E1DC3BE93AF Let $\pi \colon Y\rightarrow X$ be a blow-up with connected smooth center of codimension at least $2$ with exceptional divisor $E$. Then there is a natural identification

73D0C455ED1D 20.1.3

\begin{equation} \mathrm{H}^{1,1}(Y,\mathbb {R})=\mathrm{H}^{1,1}(X,\mathbb {R})\oplus \mathbb {R}\{ E\} . \end{equation}

See [RYY19] for a much more general result.

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@misc{pome-tag-2C74B684280C,
  author = {{Pome contributors}},
  title = {20.1.1 The notion of b-divisors},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/2C74B684280C/}
}

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20.1.1 The notion of b-divisors2C74B684280C

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20.1.1 The notion of b-divisors`2C74B684280C`