Let X be an (m × n)-matrix of indeterminates, and let J be the ideal generated by a set S of maximal minors of X. We construct the linear strand of the resolution of J. This linear strand is determined by the clique complex of the m-clutter corresponding to the set S. As a consequence one obtains explicit formulas for the graded Betti numbers β i,i+m (J) for all i ≥ 0. We also determine all sets S for which J has a linear resolution.2010 Mathematics Subject Classification. Primary 16E05, 13C40; Secondary 05E4…
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