6 problems

Let $C$ be the trigonal genus-three curve defined by $f(x,y)=0$, with coefficients $\mu_1,\mu_2,\mu_3,\mu_4,\mu_5,\mu_6,\mu_8,\mu_9,\mu_{12}$. For variables $x$ and $y$, write…

Let $g$ be even, let $B$ be a base curve not entirely contained in the Maroni divisor, and let $X\to B$ be a family whose singular members belong only to…

Let $C$ be a cyclic trigonal curve, and let $xi_p^1,\ldots,\xi_p^l$ denote the indicated tangent directions at a point $p$, with $l<2g-2$. An asymptotic direction is a direction an…

A dessin d'enfant is a combinatorial object associated with a trigonal curve; it is maximal when it has one singular fiber in each region and is connected. Deformation conjecture.…

Exhaustiveness conjecture. Tables and should exhaust all possibilities with $N\ge7$.

A real trigonal curve is a curve $\CC\subset\Sigma_k$ in a real Hirzebruch surface, where $\pr\colon\Sigma_k\to\Cp1$ is the ruling and $\conj$ denotes the real structure. Quasi-sim…