Restricting linear syzygies: algebra and geometry

Details Restricting linear syzygies: algebra and geometry Restricting linear syzygies: algebra and geometry

2004-04-28

arxiv.org/abs/math/0404516v1

Mathematics

Algebraic Geometry

26 pages, Plain TeX + diagrams.tex

Scientific paper

In this paper we derive geometric consequences from the presence of a long strand of linear syzygies in the minimal free resolution of a closed scheme in projective space whose homogeneous ideal is generated by quadrics. These consequences are given in terms of intersections with arbitrary linear subspaces. We use our results to bound homological invariants of some well-known projective varieties, to give a combinatorial characterization of quadratic monomial ideals with a long strand of linear syzygies, etc

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