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Inverting Reid’s exact plurigenera formula. (English) Zbl 0661.14013
The main result is:
Let P: \({\mathbb{N}}\to {\mathbb{Z}}\) be an arithmetic function such that \(P(n)=\chi ({\mathcal O}_ X(nK_ X))\) for some projective 3-fold X with at worst canonical singularities. Then the record (i.e. \(K^ 3_ X\), \(\chi\) (\({\mathcal O}_ X)\), the global index R and the basket \({\mathcal B}\) of singularties) of X are uniquely determined by P.
For canonical 3-folds this arithmetic function corresponds to the plurigenera and for \({\mathbb{Q}}\)-Fano 3-folds to the anti-plurigenera. This theorem shows that the minimal model of X has a unique record.
Reviewer: A.R.Fletcher

14E30 Minimal model program (Mori theory, extremal rays)
14J30 \(3\)-folds
Full Text: DOI EuDML
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