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)
Three motifs, R-helix, antiparallel-sheet, and-turn, account for most of the regular secondary structure observed in folded proteins. 1 Short peptides that adopt a defined secondary structure in solution have been used to examine the origins of R-helix 2 and-turn 3 stability, but this approach has been difficult to implement for a-sheet. 4-Hairpins, which… (More)
This paper describes how to compute equations of plane models of minimal Du Val double planes of general type with pg = 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.
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)
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)
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)