 Classically the theta characteristics were divided into these two kinds, odd and even, according to the value of the Arf invariant of a certain quadratic form "Q" with values mod 2.Thus in case of "g" = 3 and a plane quartic curve, there were 28 of one type, and the remaining 36 of the other; this is basic in the question of counting bitangents, as it corresponds to the 28 bitangents of a quartic.The geometric construction of "Q" as an intersection form is with modern tools possible algebraically.