Decomposability of local determinantal representations of hypersurfaces

Research output: Working paper/PreprintPreprint

10 Downloads (Pure)

Abstract

Let M be a matrix whose entries are power series in several variables and determinant det(M) does not vanish identically. The equation det(M)=0 defines a hypersurface singularity and the (co)-kernel of M is a maximally Cohen-Macaulay module over the local ring of this singularity. Suppose the determinant det(M) is reducible, i.e. the hypersurface is locally reducible. A natural question is whether the matrix is equivalent to a block-diagonal or at least to an upper-block-triangular. (Or whether the corresponding module is decomposable or at least is an extension.) We give various necessary and sufficient criteria. Two classes of such matrices of functions appear naturally in the study of decomposability: those with many generators (e.g. maximally generated or Ulrich maximal) and those that descend from birational modifications of the hypersurface by pushforwards (i.e. correspond to modules over bigger rings). Their properties are studied.
Original languageEnglish
PublisherarXiv:1009.2517 [math.AG]
StatePublished - 13 Sep 2010

Keywords

  • math.AG
  • math.AC
  • math.RT

Fingerprint

Dive into the research topics of 'Decomposability of local determinantal representations of hypersurfaces'. Together they form a unique fingerprint.

Cite this