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- Carlos Rito
- 2005

We classify surfaces of general type S with p g = q = 1 having an involution i such that S/i is non-ruled and the bicanonical map of S factors through the natural cover S → S/i. We prove that the minimal model of S/i is either a K3 surface or a surface of Kodaira dimension 1 (in this last case S has a genus 2 fibration). We also show that these cases do… (More)

- Carlos Rito
- Math. Comput.
- 2010

This paper describes how to compute equations of plane models of minimal Du Val double planes of general type with p g = q = 1 and K 2 = 2,. .. , 8. A double plane with K 2 = 8 having bicanonical map not composed with the associated involution is also constructed. The computations are done using the algebra system Magma.

- Carlos Rito
- 2008

In this paper some numerical restrictions for surfaces with an involu-tion are obtained. These formulas are used to study surfaces of general type S with pg = q = 1 having an involution i such that S/i is a non-ruled surface and such that the bicanonical map of S is not composed with i. A complete list of possibilities is given and several new examples are… (More)

- Carlos Rito
- 2008

Let S be a Todorov surface, i.e., a minimal smooth surface of general type with q = 0 and pg = 1 having an involution i such that S/i is birational to a K3 surface and such that the bicanonical map of S is composed with i. The main result of this paper is that, if P is the minimal smooth model of S/i, then P is the minimal desingularization of a double… (More)

- Carlos Rito
- 2009

This paper contains an algorithm, implemented in Magma, to compute singular plane algebraic curves. Two Magma functions are given: one computes linear systems of curves with non-ordinary singularities and the other computes a scheme of points such that there is a given degree plane curve with given singularities at these points. Some examples are presented… (More)

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