Type: Article
Publication Date: 1974-01-01
Citations: 89
DOI: https://doi.org/10.1090/s0002-9947-1974-0419439-2
We construct a formal versal equisingular deformation of a plane algebroid curve (in characteristic zero), and show it is smoothly embedded in the whole deformation space of the singularity. Closer analysis relates equisingular deformations of the curve to locally trivial deformations of a certain (nonreduced) projective curve. Finally, we prove that algebraic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>π<!-- π --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\pi _1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the complement of a plane algebroid curve remains constant during formal equisingular deformation.