A no-go theorem for special Ulrich bundles, with a complement on primary Burniat surfaces

Cristian Anghel, Filip Chindea

Let $X$ be a smooth projective surface with $p_g=0$, and let $H$ be an ample divisor with $h^0({\mathcal{O}}_X(H))\ne 0$, $\chi ({\mathcal{O}}_X(H))\ge q$, and $h^1({\mathcal{O}}_X(H))\ne 0$…