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3. Special degeneration


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      Problem 3.1.

      (C. Xu) Conj: Given a klt Fano variety $X$, there is a bounded family of special degeneration of $X$. The local (global?) version of Higher Rank Finite Generation Conjecture (HRFG) implies this one.


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          Problem 3.2.

          (I. Cheltsov) What about Manetti surfaces? $\mathbb{P}^2 \rightsquigarrow \mathbb{P}^2(a^2,b^2,c^2) , a^2+b^2+c^2=3abc$.


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              Problem 3.3.

              (Z. Zhuang) Can you get the finite wall-chamber structure from global HRFG Conjecture?


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                  Problem 3.4.

                  (Y. Liu) There exists special degeneration $\mathbb{P}^2 \rightsquigarrow \mathbb{P}(1,1,4), \mathbb{P}(1,4,25), X_{26} \subset \mathbb{P}(1,2,13,25)$ (Ascher-DeVleming-Liu). Are there other special degeneration of $\mathbb{P}^2$?


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                      Problem 3.5.

                      (I. Cheltsov) Given a del Pezzo surface filtrations over a curve (Mori fiber space), assume all fibers are irreducible, what are the singularities of the central fiber? Conj: bounded irregularity.


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                          Problem 3.6.

                          (C. Li) Find explicit description of isotrivial degeneration $\mathbb{P}^2 \rightsquigarrow \mathbb{P}(a^2,b^2,c^2)$.

                              Cite this as: AimPL: K-stability and related topics, available at http://aimpl.org/kstability.