8 problems

Let $X$ be a minimal surface of general type and maximal Albanese dimension. The Severi equality characterization states that … if and only if the canonical model of $X$ is a flat…

Let $V$ be the double-cover variety of type $((0),1)$, with conic-bundle projection $q\colon V\to{\mathbb P}$. Let $\operatorname{Bir}(V/{\mathbb P})$ denote the group of fiber-wis…

Let $V$ be the variety of type $((1),(0))$, birationally realized as a double space of index $2$ with a pencil of hyperplanes. For each codimension-two subspace…

Let $G\subset{\mathbb P}$ be general, let $F\to G$ be the associated Fano double cover, and set $V\cong F\times{\mathbb P}^1$. The projection $q\colon V\to F$ is a conic-bundle str…

Let $G$ be the group acting in the above setup, and let $a_i$ and $x_i$ be the coefficients and coordinates defining the quadratic potential … Here $\operatorname{MF}$ denotes the…

Let $V$) be a Fano variety, let $\mathcal{L}$ be an ample line bundle on $V$ with $r\mathcal{L}\sim_{\mathbb{Q}}-K_V$ for some $r>1$, and let $B$ be an effective divisor with…

Basic rigid local Langlands conjecture. There is a commutative diagram with horizontal bijections

Let $Y$ and $Y^{\vee}$ be fibers of the gauge-fixed double-cover families associated with dual nef-partitions on toric varieties $X$ and $X^{\vee}$, respectively. Double-cover mirr…