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2 results

  • Deformation theory of rank one maximal Cohen–Macaulay modules on hypersurface singularities and the Scandinavian complex

  • Runar Ile
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 2 / March 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 435-446
    Print publication:
    March 2004
    • Article
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  • We show that the deformation functor of a maximal Cohen–Macaulay module M = coker($\phi$) over the hypersurface singularity det($\phi$) is given by deformations of the presenting matrix which keep the determinant constant. A simplified expression for an edge map in the canonical five-term exact sequence to a change of rings spectral sequence is obtained, including the tangent and obstruction spaces (H1 and H2). We relate the edge map to the Scandinavian complex$\mathcal{S}$ of $\phi$ which yields relations between the homology of $\mathcal{S}$ and Hi for i = 1, 2. This gives (infinitesimal) rigidity and non-rigidity results and a dimension estimate for the formally (mini-)versal formal hull H of the deformation functor.