arXiv subjects

M. Mendes Lopes

Publications and source records attributed to M. Mendes Lopes.

3 recordsLinked to original sources

arXiv2000

The bicanonical map of surfaces with $p_g=0$ and $K^2 \geq 7$

A minimal surface of general type with $p_g(S)=0$ satisfies $1\le K^2\le 9$ and it is known that the image of the bicanonical map $\fie$ is a surface for $K_S^2\geq 2$, whilst for $K^2_S\geq 5$, the bicanonical map is always a morphism. In this paper it is shown that $\fie$ is birational if $K_S^2=9$ and that the degree of $\fie$ is at most 2 if $K_S^2=7$ or $K_S^2=8$. By presenting two examples of surfaces $S$ with $K_S^2=7$ and 8 and bicanonical map of degree 2, it is also shown that this result is sharp. The example with $K_S^2=8$ is, to our knowledge, a new example of a surface of general type with $p_g=0$.

math.AG↗

arXiv1999

A connected component of the moduli space of surfaces of general type with $p_g=0$

Let S be a minimal surface of general type with $p_g(S)=0$ and such that the bicanonical map $ϕ:S\to \pp^{K^2_S}$ is a morphism: then the degree of $ϕ$ is at most 4 and if it is equal to 4 then $K^2_S\le 6$. Here we prove that if $K^2_S=6$ and $°ϕ=4$ then S is a so-called {\em Burniat surface}. In addition we show that minimal surfaces with $p_g=0$, $K^2=6$ and bicanonical map of degree 4 form a 4-dimensional irreducible connected component of the moduli space of surfaces of general type.

math.AG↗

arXiv1998

Triple canonical surfaces of minimal degree

We classify completely the surfaces of general type whose canonical map is 3-to-1 onto a surface of minimal degree in projective space. These surfaces fall into 5 distinct classes and we give explicit examples belonging to each of these classes. As far as we know, one of the examples thus constructed was unknown and it is a surface whose canonical system has two infinitely near base points.

math.AG↗