English

Homological flips and homological flops

Algebraic Geometry 2020-02-04 v3

Abstract

We introduce a notion of homological flips and homological flops. The former includes the class of all flips between Gorenstein normal varieties; while the latter includes the class of all flops between Cohen-Macaulay normal varieties whose contracted variety is quasi-Gorenstein. Our main theorem shows that certain local cohomology complexes are dual to each other under homological flips/flops. We give some preliminary applications of this duality to relate the derived categories under flip/flop. Further applications are in [Yeu20b].

Keywords

Cite

@article{arxiv.1907.06190,
  title  = {Homological flips and homological flops},
  author = {Wai-Kit Yeung},
  journal= {arXiv preprint arXiv:1907.06190},
  year   = {2020}
}

Comments

29 pages; some parts split out as independent papers arXiv:2001.08795 and arXiv:2001.10431; some mistakes corrected; some results improved

R2 v1 2026-06-23T10:20:30.225Z