arXiv subjects

Gianni Sacchiero

Publications and source records attributed to Gianni Sacchiero.

2 recordsLinked to original sources

arXiv2012

On the singularities of surfaces ruled by conics

We classify the singularities of a surface ruled by conics: they are rational double points of type $A_n$ or $D_n$. This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by conics. We determine also the family of such surfaces which are birational models of a given surface ruled by conics and obtained in a "minimal way" from it.

math.AG↗

arXiv2012

Stratification of the moduli space of four--gonal curves

Let $X$ be a smooth irreducible projective curve of genus $g$ and gonality 4. We show that the canonical model of $X$ is contained in a uniquely defined surface, ruled by conics, whose geometry is deeply related to that of $X$. This surface allows us to define four invariants of $X$ and hence to stratify the moduli space of four-gonal curves by means of closed irreducible subvarieties whose dimensions we compute.

math.AG↗