This problem is related to a conjecture of Kobayashi and Zaidenberg which states that for a sufficiently general curve D ⊂ P of degree d ≥ 5, as general in the sense that D lies in |OP2(d)| ∼= P d(d+3)/2 with countably many closed proper subvarieties removed, the affine variety P\D is hyperbolic. One necessary condition for P\D being hyperbolic is that there is no rational curve C ⊂ P meeting D...

Given a smooth nonhyperelliptic curve C and a pencil g d of degree d on C, let X be the curve parametrizing pairs of points in divisors of g d (see the paper for the precise scheme-theoretical definition). We prove that if X deforms infinitesimally out of the jacobian locus with JC then either d = 4 or d = 5, dimH(g 5 ) = 3 and C has genus 5 or genus 4 and only one g 3 .

An algorithm is presented to approximate planar offset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bézier curve segments within the tolerance . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic Bézier curve segments. For a p...

introduction: nowadays,  considerable developments  in  the field  of  radiotherapy have  been  achieved.  they  include  the  advances  made  in  the  equipments  and  treatment  planning  techniques  which  require  highly complex calculations. such achievements have made it possible to treat cancer patients not only  with  higher  radiation  dose  but  also  with  higher  precision  and  con...

let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (respectively, any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that there exists a pseudo-holomorphic curve (a Hurwitz curve) in CP whose fundamental group of the complement is not Hopfian and, respectively, this group is not...