Simple singularities of curves (Q2714681)

The purpose of this paper is to study the simple singularities of curves. The simple singularities of curves in the plane have been classified by J. W. Bruce and T. Gaffney and those of curves in three-space, by C. Gibson and C. Hobbs. NEWLINENEWLINENEWLINEThe author of this paper classifies the simple curve singularities in spaces of any dimension up to stable equivalence. The author proves that almost all those singularities whose Taylor series from a term of degree 2 or 3 or has the form NEWLINE\[NEWLINEx=t^6,\quad y=t^6,\quad z_id=0 \pmod {t^7}NEWLINE\]NEWLINE are simple, and that these curves there exist 32 sporadic simple curves.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00069].