Curves of maximum genus in range A and stick-figures

Abstract

In this paper we show the existence of smooth connected space curves not contained in a surface of degree less than <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m"> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding="application/x-tex">m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, with genus maximal with respect to the degree, in half of the so-called range A. The main tool is a technique of deformation of stick-figures due to G. Fløystad.