4 problems

Let $F:\mathbb{C}^4\rightarrow\mathbb{C}^4$ be the birational map … let $\phi(x_1,x_2,x_3,x_4)=x_1x_4-x_2x_3$, and for generic $c\in\mathbb{C}$ let $X_c\subset\mathbb{P}^4$ be the…

Birational OY-invariant conjecture. The function $\EuScript{Y}^{\mathrm{B}}\colon\mathcal{A}^{\mathrm{B}}(\mathsf{A}^n)\to\mathbb{R}_{>0}$ is invariant under both…

Birational type B homomesy conjecture. The statistics $h^{\mathrm{B}}_i\colon \mathcal{A}^{\mathrm{B}}_{\kappa}(\mathsf{B}^n)\to \mathbb{R}_{>0}$, for $1\leq i\leq 2n-1$, and…

Rigidity conjecture. Then the family $(\varphi_\alpha\Phi_n)_{\alpha\in U}$ is holomorphically trivial.