For all g â‰¥ 2 there is a Riemann surface of genus g whose automorphism group has order 8g+8, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola andâ€¦ (More)

Let R be a real closed field and n â‰¥ 2. We prove that: (1) for every finite subset F of R, the semialgebraic set R \ F is a polynomial image of R; and (2) for any independent linear forms l1, . . . ,â€¦ (More)

We obtain new necessary conditions for an n-dimensional semialgebraic subset of R to be a polynomial image of R. Moreover, we prove that a large family of planar bidimensional semialgebraic sets withâ€¦ (More)

In this work we present a new polynomial map f := (f1, f2) : R â†’ R whose image is the open quadrant Q := {x > 0, y > 0} âŠ‚ R. The proof of this fact involves arguments of topological nature that avoidâ€¦ (More)

We compute the period matrices of the Riemann surfaces given by the equations w = z âˆ’ 1 (Accolaâ€“Maclachlan surfaces) and w = z(z âˆ’ 1)gâˆ’1(z + 1) (Kulkarni surfaces). Furthermore, we obtain the triplesâ€¦ (More)

Let X be a symmetric compact Riemann surface whose full group of conformal automorphisms is cyclic. We derive a formula for counting the number of ovals of the symmetries of X in terms ofâ€¦ (More)

We consider normal (possibly) branched, finite-sheeted coverings Ï€ : X â†’ Xâ€² between hyperelliptic real algebraic curves. We are interested in the topology of such coverings and also in describingâ€¦ (More)