9 problems

Rational degree conjecture. There exists a $\mathbb{Q}$-valued topological degree ${\rm deg}(f)$ such that

Let $V$ be a surface with $p_g(V)>0$, let $K$ be an effective canonical divisor, and fix $m\in H^2(V,\mathbb{Z})$. Let … be the zero-cycle on…

Let $(V,g)$ be a surface with a Kähler metric $g$, let $m\in H^2(V,\mathbb{Z})$, and let $\beta$ be a real closed $2$-form of type $(1,1)$. Let $\tau$ be a $Spin^c(4)$-structure re…

Let $X$ be a variety, let $V$ be a convex vector bundle on $X$, and let $Y\hookrightarrow X$ be the zero locus of a regular section of $V$. For $\beta\in H_2(X,\mathbb{Z})$ and…

Let $W$ be the coarse projective variety in the KSBA moduli problem, let ${\mathfrak W}\to W$ be a $\mu_N$-gerbe, and let $M$ be the associated KSBA moduli space. Suppose that the…

Let $\boldsymbol{\mathfrak{Y}}$ be a quasi-smooth derived Artin stack, write $\mathfrak{Y}=t_0(\boldsymbol{\mathfrak{Y}})$, and let…

Let $\boldsymbol{Y}$ be a quasi-smooth derived scheme, write $Y=t_0(\boldsymbol{Y})$, and let $\widetilde{Y}=t_0(\mathbf{T}^*[-1]\boldsymbol{Y})$. The class…

Let $\tau:{\mathcal C}_+\to \mathfrak{Q}_{g,m,d,n}^{\delta_+}$ be the universal curve, with universal family of quasi-maps and wall-crossing morphism…

Let $X$ be an equivariant virtually smooth scheme with fixed-point components $X_i$, inclusion $\iota:\bigcup X_i\to X$, virtual structure sheaves…