Abstract
This paper concerns the construction of minimal varieties with small canonical volumes. The first part devotes to establishing an effective nefness criterion for the canonical divisor of a weighted blow-up over a weighted hypersurface, from which we construct plenty of new minimal $3$-folds including 59 families of minimal $3$-folds of general type, several infinite series of minimal $3$-folds of Kodaira dimension $2$, 2 families of minimal $3$-folds of general type on the Noether line, and 12 families of minimal $3$-folds of general type near the Noether line. In the second part, we prove effective lower bounds of canonical volumes of minimal $n$-folds of general type with canonical dimension $n-1$ or $n-2$. Examples are provided to show that the theoretical lower bounds are optimal in dimension at most $5$ and nearly optimal in higher dimensions.
Funding Statement
This project was supported by NSFC for Innovative Research Groups (#12121001) and National Key Research and Development Program of China (#2023YFA1010600, #2020YFA0713200). The first author was supported by National Natural Science Foundation of China (#12071078, #11731004).
Citation
Meng Chen. Chen Jiang. Binru Li. "On minimal varieties growing from quasismooth weighted hypersurfaces." J. Differential Geom. 127 (1) 35 - 76, May 2024. https://doi.org/10.4310/jdg/1717356154
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