Towards a theory of arithmetic degrees (Q1914838)

The main theme of the paper is an investigation of the arithmetic degree of projective schemes, introduced by \textit{D. Bayer} and \textit{D. Mumford} [in: Computational Algebraic Geometry and Commutative Algebra, Proc. Conf. Cortona 1991, Press, 1-48 (1993; Zbl 0846.13017)]. First the behaviour of the arithmetic degree under hypersurface sections is considered. Then an upper bound for the arithmetic degree in terms of the Castelnuovo-Mumford regularity is given and Bezout's theorem is generalized via iterated hypersurface sections. Finally, two examples are studied.