Asset Details
Do you wish to reserve the book?
On the connectedness principle and dual complexes for generalized pairs
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
On the connectedness principle and dual complexes for generalized pairs
Do you wish to request the book?
On the connectedness principle and dual complexes for generalized pairs
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
On the connectedness principle and dual complexes for generalized pairs
2023
Overview
Let
$(X,B)$
be a pair, and let
$f \\colon X \\rightarrow S$
be a contraction with
$-({K_{X}} + B)$
nef over S. A conjecture, known as the Shokurov–Kollár connectedness principle, predicts that
$f^{-1} (s) \\cap \\operatorname {\\mathrm {Nklt}}(X,B)$
has at most two connected components, where
$s \\in S$
is an arbitrary schematic point and
$\\operatorname {\\mathrm {Nklt}}(X,B)$
denotes the non-klt locus of
$(X,B)$
. In this work, we prove this conjecture, characterizing those cases in which
$\\operatorname {\\mathrm {Nklt}}(X,B)$
fails to be connected, and we extend these same results also to the category of generalized pairs. Finally, we apply these results and the techniques to the study of the dual complex for generalized log Calabi–Yau pairs, generalizing results of Kollár–Xu [Invent. Math. 205 (2016), 527–557] and Nakamura [Int. Math. Res. Not. IMRN 13 (2021), 9802–9833].
Publisher
Cambridge University Press
Subject
