arXiv subjects

E. Sernesi

Publications and source records attributed to E. Sernesi.

2 recordsLinked to original sources

arXiv2011

The symmetric square of a curve and the Petri map

Let $\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $ρ(g,1,n)$ is non-negative the Petri locus $P^1_{g,n}\subset \M_g$ has a divisorial component whose closure has a non-empty intersection with $Δ_0$. In order to prove the result we show that the scheme $G^1_n(Γ)$ that parametrizes degree $n$ pencils on a curve $Γ$ is isomorphic to a component of the Hilbert scheme parametrizing certain curves on the symmetric square $Γ_2$ of $Γ$ and we study the properties of such a family of curves.

math.AG↗

arXiv2001

Severi varieties and branch curves of abelian surfaces of type (1,3)

Let (A,L) be a principally polarized abelian surface of type (1,3). The linear system |L| defines a 6:1 covering of A onto P2, branched along a curve B of degree 18 in P2. The main result of the paper is that for general (A,L) the curve B irreducible, admits 72 cusps, 36 nodes or tacnodes, each tacnode counting as two nodes, 72 flexes and 36 bitangents. The main idea of the proof is to use the fact that for a general (A,L) of type (1,3) the closure of the Severi variety V in |L| is dual to the curve B in the sense of projective geometry. We investigate V and B via degeneration to a special abelian surface.

math.AG↗