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2. Log rational and cluster type pairs


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      Problem 2.1.

      If $X$ is rational Fano and there exists $D\in|-K_X|$ with coregularity $0$, is $X$ log rational? 2-18? (OK if $X$ general in def class.)


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          Problem 2.2.

          Does cluster type varieties $X/k$ lift to $W_2(k)$, where $\operatorname{char} k=p$?


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              Problem 2.3.

              For crepant birational log CY pairs $(\mathbb{P}^3,D)\dashrightarrow(\mathbb{P}^3,D')$, where $D$ and $D'$ have ADE singularities, are $D$ and $D'$ birational?

              Note: There are examples where $D\simeq D'$ while $(\mathbb{P}^3,D)$ and $(\mathbb{P}^3,D')$ are not crepant birationally equivalent.

              Lattice Theory of different quartic models of same K3?

                  Cite this as: AimPL: Higher-dimensional log Calabi-Yau pairs, available at http://aimpl.org/higherdimlogcy.