Wang's maximal-Betti-number conjecture for smooth Calabi-Yau varieties

Let $W^{(n)}$ be the smooth, projective Calabi-Yau $n$-fold constructed in the paper, and write $b_i(W^{(n)})$ for its Betti numbers and $\chi(W^{(n)})$ for its Euler characteristic.

Wang's maximal-Betti-number conjecture. The variety $W^{(n)}$ has the largest sum of Betti numbers among smooth, projective Calabi-Yau $n$-folds. When $n$ is odd, it also has the smallest negative Euler characteristic among such varieties.

The conjecture is motivated by the analogous orbifold Betti-number calculation of Esser, Totaro, and Wang and by Yasuda's result relating orbifold cohomology to the cohomology of a crepant resolution. Its general validity remains open.