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11. Other problems


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      Problem 11.1.

      (Z. Patakfalvi) Consider f: \mathfrak{X} \to T(smooth projective curve), assume the general fiber is unifrom K-stable. Let c_{nef}:= minimum of c such that -K_{\mathfrak{X}/T}+c \cdot f^* (t) is nef. Find an effective upper bound of c_{nef} in terms of \delta, \mathrm{vol} of general fiber.


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          Problem 11.2.

          (I. Cheltsov, A. Castravet, S. Donaldson) Let X be a smooth Fano variety, \mathrm{Pic}(X)=\mathbb{Z}(-K_X). Is X always K-semistable?

          (S. Donaldson) Is the moduli spcae of vector bundles on a curve K-(semi)stable?

          (C. Araujo) What about moduli space of parabolic bundles over \mathbb{P}^1 with half weight?


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              Problem 11.3.

              (C. Araujo) Let X be a smooth Fano variety. Let V denote the variety of minimal degree rational curves through a general point. Does the K-(semi)stability of X implies special properties of V?


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                  Problem 11.4.

                  (Y. Liu) Explicitly describe the K-moduli compactification of (\mathbb{P}^1 \times \mathbb{P}^1, c \cdot C), where C \in |\mathscr{O}(3,3)|, 0 < c < 2/3.

                  \cdot Birational model of M_4,

                  \cdot When c=1/2, a divisor of this K-moduli space isomorphic with K-moduli space of dP_1.

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