Speaker
Rita Pardini
(Università di Pisa)
Description
An I-surface (also called a (1,2)-surface) is a complex projective surface with $K^2=1$, $h^2(O)=2$ and ample canonical class. Gorenstein stable I-surfaces are hypersurfaces of degree 10 in $\mathbb{P}(1,1,2,5)$. In order to study stable I-surfaces of index 2 we introduce generalized Gorenstein spin curves, namely pairs $(C,L)$ where $C$ is a Gorenstein curve with ample canonical class and $L$ is a torsion-free rank 1 sheaf on $C$ with $\chi(L)=0$ admitting a generically injective map $L\otimes L\to\omega_C$. We obtain a complete classification of such pairs with C reduced of genus 2 and derive from it the classification of stable I-surfaces of index 2 with a reduced canonical curve.
