7 problems

Let $S$ be a product-quotient surface of general type, and let $X$ be its quotient model. A singular point of $X$ has a multiplicity in the usual sense. Bounded-multiplicity conjec…

Let $S$ be a product-quotient surface of general type, let $X$ be its quotient model, and let $p_g(S)$ and $q(S)$ denote its geometric genus and irregularity. Let $\gamma(X)$ be th…

A product-quotient surface is a surface obtained as the minimal resolution of a quotient model $(C_1\times C_2)/G$. The paper has constructed 75 families of product-quotient surfac…

Let $S$ be a product-quotient surface, with geometric genus $p_g(S)$ and invariant $4gamma4$. Minimality conjecture. $S$ is minimal if and only if … The paper proves this when…

Let $S$ be a regular product-quotient surface with quotient model $X$, and let $H^2(X)$ be viewed inside $H^2(S)$. Write the Zariski decomposition of the canonical divisor as … and…

Let $S$ be a regular product-quotient surface with invariants $p_g$, $q$, and $c:=\gamma+p_g\in\mathbb{N}$, where $c$ is half the codimension of the subspace of $H^2(S,\mathbb{C})$…

Let $S$ be a regular product-quotient surface, and let $\gamma(S)$ be the invariant associated with its product-quotient structure. An exceptional curve of the first kind is a smoo…