Generating functions for all cohomologies on Calabi–Yau threefolds with infinitely many flops (non–Mori dream spaces)
Establish that for the general complete intersection Calabi–Yau threefold X with configuration matrix [P^4|2 0 1 1 1; P^4|0 2 1 1 1], whose effective cone decomposes into a doubly infinite sequence of Mori chambers, the infinite sums of rational functions G_n and C_n defined by the authors generate all cohomology series via the stated expansion rules and truncations—yielding CS^0(X, O_X), CS^1(X, O_X), CS^2(X, O_X), and CS^3(X, O_X) as claimed.
References
Conjecture 7. Let $X$ be a general complete intersection Calabi-Yau threefold in the deformation family given by the configuration matrix matrix{P4 \ P4}{2& 0& 1 & 1& 1\ 0& 2& 1& 1& 1} and let $H_1 = \mathcal O_{P4\times P4}(1,0)|_X$ and $H_2 = \mathcal O_{P4\times P4}(0,1)|_X$. The effective cone decomposes into a doubly infinite sequence of Mori chambers corresponding to the nef cones of isomorphic Calabi-Yau threefolds connected to $X$ through a sequence of flops, of the form $K{(n)} = R_{\geq 0} (a_{n+1} H_1-a_{n}H_2) + R_{\geq 0} (a_n H_1-a_{n-1}H_2)$, with $a_n$ given by ... such that $K{(0)}={\rm Nef}(X)$. A generating function for all line bundle cohomology dimensions can be written in terms of the functions ... as follows: ...