Boundedness of ($\epsilon ,n$)-Complements for projective generalized pairs of Fano type

Abstract

We show the existence of $(\epsilon ,n)$-complements for $(ε,\Rr)$-complementary projective generalized pairs of Fano type $(X,B+M)$ when either the coefficients of $B$ and ${\mu }_j$ belong to a finite set or the coefficients of $B$ belong to a DCC set and $M^{\prime }\equiv 0$, where $M^{\prime }=\sum {\mu }_j{M}_j^{\prime }$ and $M_j^{\prime }$ are b-Cartier nef divisors.

17 pages, comments are welcome! arXiv admin note: text overlap with arXiv:2003.04237

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