Estimates are obtained for the degrees of minimal syzygies of quotient algebras of polynomial rings. For a class that includes Koszul algebras in almost all characteristics, these degrees are shown to increase by at most two from one syzygy module to the next one. Even slower growth is proved if, in addition, the algebra satisfies Green and Lazarsfeld’s condition Nq with q≥2.
Subadditivity of syzygies of Koszul algebras
CONCA, ALDO;
2014-01-01
Abstract
Estimates are obtained for the degrees of minimal syzygies of quotient algebras of polynomial rings. For a class that includes Koszul algebras in almost all characteristics, these degrees are shown to increase by at most two from one syzygy module to the next one. Even slower growth is proved if, in addition, the algebra satisfies Green and Lazarsfeld’s condition Nq with q≥2.
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