论文标题
Fano三倍和K3表面上的带束带的模量9属。
Moduli spaces of sheaves on Fano threefolds and K3 surfaces of genus 9
论文作者
论文摘要
复杂的平滑Prime Fano三倍的$ x $属$ 9 $通过投影双重性与四分平的平面曲线$γ$相关。我们使用此设置来研究排名$ 2 $稳定的滑轮的限制，并在$ x $上开处方的Chern类，以$ x $，to antoanical $ k3 $ k3 $ s surface $ s \ s \ subset x $。 Varying the threefold $X$ containing $S$ gives a rational Lagrangian fibration $$\mathcal{M}_S(2,1,7) \dashrightarrow \mathbb{P}^3$$ with generic fibre birational to the moduli space $\mathcal{M}_X(2,1,7)$ of sheaves on $X$.此外，我们证明，这种合理振动扩展到了$ \ Mathcal {M} _s {M} _s _s（2,1,7）$上的Birational Model $ \ Mathcal {M} $上的实际振动。 在最后一部分中，我们使用Bridgeland稳定性条件来展示$ \ Mathcal {M} _s _s（2,1,7）$的所有$ K $平滑的模型，这些模型由本身和$ \ Mathcal {M} $组成。我们证明了这些模型是通过flop关联的，我们描述了$ \ Mathcal {M} _S（2,1,7）$的正，可移动和NEF锥。
A complex smooth prime Fano threefold $X$ of genus $9$ is related via projective duality to a quartic plane curve $Γ$. We use this setup to study the restriction of rank $2$ stable sheaves with prescribed Chern classes on $X$ to an anticanonical $K3$ surface $S\subset X$. Varying the threefold $X$ containing $S$ gives a rational Lagrangian fibration $$\mathcal{M}_S(2,1,7) \dashrightarrow \mathbb{P}^3$$ with generic fibre birational to the moduli space $\mathcal{M}_X(2,1,7)$ of sheaves on $X$. Moreover, we prove that this rational fibration extends to an actual fibration on a birational model $\mathcal{M}$ of $\mathcal{M}_S(2,1,7)$. In a last part, we use Bridgeland stability conditions to exhibit all $K$-trivial smooth birational models of $\mathcal{M}_S(2,1,7)$, which consist in itself and $\mathcal{M}$. We prove that these models are related by a flop, and we describe the positive, movable and nef cones of $\mathcal{M}_S(2,1,7)$.
