Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Geometry

arXiv:1907.06190 (math)
[Submitted on 14 Jul 2019 (v1), last revised 1 Feb 2020 (this version, v3)]

Title:Homological flips and homological flops

Authors:Wai-Kit Yeung
View PDF
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].
Comments: 29 pages; some parts split out as independent papers arXiv:2001.08795 and arXiv:2001.10431; some mistakes corrected; some results improved
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1907.06190 [math.AG]
  (or arXiv:1907.06190v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1907.06190

Submission history

From: Wai-Kit Yeung [view email]
[v1] Sun, 14 Jul 2019 08:45:51 UTC (94 KB)
[v2] Mon, 20 Jan 2020 23:16:22 UTC (47 KB)
[v3] Sat, 1 Feb 2020 00:44:47 UTC (47 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.AG
< prev   |   next >
new | recent | 2019-07
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)