Differential geometry “in the large” of plane algebraic curves and integral formulas for invariants of singularities

We generalize the Plücker formula for the number of inflection points of a complex projective curve and derive a formula for the number of sextatic points of such a curve. We also obtain an upper estimate for the number of vertices of a real algebraic curve. The proof uses a new result related with integration on the Euler characteristic. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 255–268. Translated by N. Yu. Netsvetaev.