33 problems

Maulik–Yun's conjecture. The perverse filtration and the Lefschetz filtration are opposite:

Multiplicative splitting conjecture. There exists such a splitting that is multiplicative under cup product:

Let $C$ be a rational integral projective curve with a unique irreducible planar curve singularity $(C,0)$, let $\overline{J}C$ be its compactified Jacobian, and let…

Galashin–Lam's conjecture. There exists a non-algebraic deformation retract

Let $C_0$ be the central curve in the setting of Theorem 0.8, and let $\phi$ and $\phi'$ be nondegenerate stability conditions. Write $\overline{J}^{\phi}_{C_0}$ and…

Kononov–Moreira–Lim–Pi conjecture. The associated graded group

Let $\bar J_{\mathcal C} \xrightarrow{\pi} B$ be a compactified Jacobian fibration associated to a flat family of integral projective locally planar curves of arithmetic genus $g$…

Let $C$ be an irreducible pseudo-stable genus $2$ curve with one node and normalization $\widetilde{C}$, and let $V_0$ be the associated K-polystable $(2,2)$-complete intersection.…

Let $Z=\{f(x,y)=0\}\subset\mathbb{C}^2$ be a curve with a unibranch singularity at $0$, and let $K=K_Z$ denote its link, which is a knot. Let $\delta$ be the Milnor number of…

Let $m,n$ be coprime positive integers, let $C_{\frac{m}{n}}$ be the closure of $y^m=x^n$ in $\mathbb{P}^2$, and let $J_{\frac{m}{n}}$ be its compactified Jacobian. Let $P$ be the…

Let $\pi:\overline{J}_C\to B$ be a Lagrangian compactified Jacobian fibration as in the motivic Beauville decomposition conjecture, with motivic summands $h_{2i}(\overline{J}_C/B)$…

Let $\pi:\overline{J}_C\to B$ be as in the motivic Beauville decomposition conjecture, and let $\operatorname{Corr}^k_B(\overline{J}_C,\overline{J}_C)$ denote the degree-$k$ relati…

Let $\pi:\overline{J}_C\to B$ be the compactified Jacobian fibration associated with a flat family of integral projective locally planar curves of arithmetic genus $g$ over a nonsi…

Let $C$ be a complex integral projective curve whose normalization has genus zero and whose unique planar singularity is locally given by $f(x,y)=0$. Let…

Let $R$ be the complete local ring of a complex algebraic plane curve germ, with normalization $S$. Let $\mathcal{C}\operatorname{ptPic}$ be its compactified Picard scheme, let…

Let $M_{r,\chi}$ be the moduli space of one-dimensional stable sheaves on $\mathbb{P}^2$ with support in the class $[rH]$ and Euler characteristic $\chi$, where $H$ is the hyperpla…

Let $(r_1,s_1),\ldots,(r_{\ell},s_{\ell})$ be a sequence of characteristic pairs for an algebraic curve. Starting with $f_{\ell+1}:=p_1\in\Lambda$, recursively apply the operators…

Consider a curve with parametrization … where $\operatorname{GCD}(m,n)=\operatorname{GCD}(d,s)=1$ and $\lambda\neq 0$. Let $J_{\Delta}$ be the stratum of its compactified Jacobian…

Let $C$ be an extended ADE curve with type $\tilde D_n$, $\tilde E_6$, $\tilde E_7$, or $\tilde E_8$, and write … Let $J$ be the Jacobian and let $\mathcal M$ be the moduli space o…

Let $\Pit_{k,n}$ be the torus quotient and let $J_{k,n-k}$ be the compactified Jacobian of the plane curve singularity $x^k=y^{n-k}$. Their cohomology carries a weight filtration a…

Let $A$ be an Abelian surface of Picard rank one, let $\tau$ be the involution defining the quotient, and let $C\subset A$ be an integral $\tau$-invariant curve of geometric genus…

Let $C$ be a curve with rational normalization and a unique planar singularity. Let $\mathcal{J}(C)$ be its compactified Jacobian, let $\delta=\dim \mathcal{J}(C)$, and let…

Let $C$ be a complex curve with rational normalization and one planar singularity, and let $\mathcal{J}(C)$ be its compactified Jacobian. Van Straten's vanishing conjecture. The od…

Let $\Gamma\tsubset\mathbb{Z}_{\ge 0}$ be a submonoid, let $C_\Gamma$ be the associated projective toric curve, let $\mathcal{O}_\Gamma$ be the Artinian coordinate ring of…

Let $\mathcal{C}/\mathcal{B}'$ be the family of curves and let $\mathcal{J}(\mathcal{C}/\mathcal{B}')$ be its relative compactified Jacobian. Let $h$ denote the projection to…