Rational connectedness conjecture for quasi-Campana pairs

Let (X,D\mathbfsymbolm)(X,D_{\mathbfsymbol{m}}) be a Campana pair, where D\mathbfsymbolmD_{\mathbfsymbol{m}} is its boundary divisor, and assume that the log-anticanonical divisor KXD\mathbfsymbolm-K_X-D_{\mathbfsymbol{m}} is ample. Let (X,M)(X,M) be a proper quasi-Campana pair for (X,D\mathbfsymbolm)(X,D_{\mathbfsymbol{m}}). Rational connectedness conjecture for quasi-Campana pairs. The pair (X,M)(X,M) is rationally connected. This prediction extends rational connectedness from log Fano Campana pairs to their proper quasi-Campana pairs; no proof or disproof is supplied in the source.

Sources & referencesView supporting material

Primary source

Boaz Moerman, “Manin's conjecture for M-points”, arXiv:2512.07654 (2026).

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