Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/AMS/Regular/BBBold.js
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

3. Special degeneration

    1. 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.
        • 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.
            • Problem 3.3.

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