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A note on derived equivalences and birational geometry
Author(s) -
Calabrese John
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12039
Subject(s) - mathematics , birational geometry , functor , pure mathematics , geometry
We give a straightforward proof of the following fact. Let X and Y be two smooth (or Gorenstein) and projective varieties and let Φ : D ( X ) ↪ D ( Y ) be a fully faithful functor between their derived categories. If Φ sends a skyscraper to a skyscraper, then X and Y are birational. We also show some related results.