Rigid isotopies of real trigonal curves on Hirzebruch surfaces
by
Victor Zvonilov
Syktyvkar State University

Rigid isotopies of real trigonal curves on Hirzebruch surfaces

presented by

Victor Zvonilov

Syktyvkar State University

A rigid isotopy of plane nonsingular real algebraic curves is a path in the space of such curves of a given degree. This notion was introduced by Rokhlin in 1978. Clearly, it can be extended for real algebraic curves of a given class on a surface. First, a survey of the recent results on the rigid isotopy classification of real trigonal curves on quadrics is given. In particular, such classification for nonsingular curves of bidegree (3, 3) and (4, 3) is obtained. Besides, for these bidegrees the connected components of the space of curves with a single node or cusp are enumerated. Some of these results are our joint work with Alexander Degtyarev. Then, some solved and unsolved problems about the rigid isotopies of real trigonal curves on other Hirzebruch surfaces are discussed.

References: A.I.Degtyarev, V.I.Zvonilov. Rigid isotopy classification of real algebraic curves of bidegree (3, 3) on quadrics. Matem. Zametki, to appear.

V.I.Zvonilov. Rigid isotopy classification of real algebraic curves of bidegree (4, 3) on quadrics. Vestnik Syktyvkarskogo Universiteta, ser. 1, v. 3, 1999, p. 81-88.

Date received: May 23, 1999