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Title of Journal: Invent math

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Abbravation: Inventiones mathematicae

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Springer Berlin Heidelberg

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DOI

10.1002/cjoc.201100657

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1432-1297

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Fsingularities of pairs and Inversion of Adjuncti

Authors: Shunsuke Takagi
Publish Date: 2004/07/01
Volume: 157, Issue: 1, Pages: 123-146
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Abstract

We generalize the notions of Fregular and Fpure rings to pairs Rmathfrakat of rings R and ideals mathfraka subsetR with real exponent t0 and investigate these properties These “Fsingularities of pairs” correspond to singularities of pairs of arbitrary codimension in birational geometry Via this correspondence we prove a sort of Inversion of Adjunction of arbitrary codimension which states that for a pair XY of a smooth variety X and a closed subscheme YsubsetneqX if the restriction ZY Z to a normal ℚGorenstein closed subvariety ZsubsetneqX is klt resp lc then the pair XY+Z is plt resp lc near Z

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Other Papers In This Journal:
  1. Serre’s modularity conjecture (I)
  2. Serre’s modularity conjecture (I)
  3. Erratum to: Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space
  4. Image of Λ -adic Galois representations modulo p
  5. Representation theory of $\mathcal{W}$-algebras
  6. The Kodaira dimension of the moduli of K3 surfaces
  7. Brownian Gibbs property for Airy line ensembles
  8. Degree formula for connective K -theory
  9. Some quantitative results in $${\mathcal {C}}^0$$ symplectic geometry
  10. Convexes divisibles IV : Structure du bord en dimension 3
  11. The classification of irreducible admissible mod p representations of a p -adic GL n
  12. Some prime factorization results for type II 1 factors
  13. $\mathcal{C}^{2}$ surface diffeomorphisms have symbolic extensions
  14. On the weights of mod p Hilbert modular forms
  15. Operator-algebraic superridigity for SL n (ℤ), n ≥3
  16. Exceptional zero formulae and a conjecture of Perrin-Riou
  17. Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case
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