Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the connectedness principle and dual complexes for generalized pairs   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-Koll\'{a}r
connectedness principle, predicts that $f^{-1} (s) \cap \mathrm{Nklt}(X,B)$ has
at most two connected components, where $s \in S$ is an arbitrary schematic
point and $\mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. In this
work, we prove this conjecture, characterizing those cases in which
$\mathrm{Nklt}(X,B)$ 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 Koll\'{a}r-Xu and Nakamura.

1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an