Last syzygies of 1-generic spaces

@article{Bothmer2004LastSO,
  title={Last syzygies of 1-generic spaces},
  author={H. G. Bothmer},
  journal={Journal of Algebra},
  year={2004},
  volume={278},
  pages={360-369}
}
  • H. G. Bothmer
  • Published 2004
  • Mathematics
  • Journal of Algebra
  • Abstract We consider determinantal varieties X(γ) of expected codimension defined by the maximal minors of a matrix M(γ) of linear forms representing a linear map γ. Eisenbud and Popescu have conjectured that 1-generic linear maps γ have the property that the syzygy ideals I(s) of all last syzygies s of X(γ) coincide with IX(γ). We prove a geometric version of this conjecture: for 1-generic linear maps γ the syzygy varieties Syz(s)=V(I(s)) of all last syzygies have the same support as X(γ). 

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    E-mail address: bothmer@math.uni-hannover.de URL: http://btm8x5.mat.uni-bayreuth
    • E-mail address: bothmer@math.uni-hannover.de URL: http://btm8x5.mat.uni-bayreuth