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Refs:
- Fundamental theorems for slc pairs: https://www.math.kyoto-u.ac.jp/~fujino/funda-slc-ag-final.pdf#page=1 #resources/notes
- Links:
slc
A pair \((X, B)\) with \(X\) a reduced variety and \(B = \sum b_i B_i\) a \({\mathbf{Q}}{\hbox{-}}\)divisor is an slc pair iff
- \(X\) is \(S_2\) (?)
- \(X\) has at worst double crossings in codimension 1,
- the pair \((X^\nu, B^\nu)\) is log canonical where \(\nu: X^\nu \to X\) is the normalization and \(X^\nu, B^\nu\) are defined by \begin{align*}\nu^*(K_X + B) = K_{X^\nu} + B^\nu\end{align*} Note that one can write \(B^\nu = D + \sum B_i \nu^{-1}(B_i)\) where \(D\) is the double locus.
