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- W3092940498 abstract "A conjecture, known as the Shokurov-Kollar connectedness principle, predicts the following. Let $(X,B)$ be a pair, and let $f colon X rightarrow S$ be a contraction with $-(K_X + B)$ nef over $S$; then, for any point $s in S$, the intersection $f^{-1} (s) cap mathrm{Nklt}(X,B)$ has at most two connected components, where $mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. This conjecture has been extensively studied in characteristic zero, and it has been recently settled in that context. In this work, we consider this conjecture in the setup of positive characteristic algebraic geometry. We prove this conjecture holds for threefolds in characteristic $p> 5$, and, under the same assumptions, we characterize the cases in which $mathrm{Nklt}(X,B)$ fails to be connected." @default.
- W3092940498 created "2020-10-22" @default.
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- W3092940498 date "2020-10-16" @default.
- W3092940498 modified "2023-09-27" @default.
- W3092940498 title "Connectedness principle in characteristic $p>5$" @default.
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