Ranestad, Kristian Surfaces of degree 10 in the projective fourspace. (English) Zbl 0827.14023 Catanese, F. (ed.) et al., Problems in the theory of surfaces and their classification. Papers from the meeting held at the Scuola Normale Superiore, Cortona, Italy, October 10-15, 1988. London: Academic Press. Symp. Math. 32, 271-307 (1991). The study of smooth surfaces in \(\mathbb{P}^4\) goes back to the Italians at the turn of the century.In the special case of surfaces in \(\mathbb{P}^4\), where smoothness imposes additional relations among the invariants of the surface, a complete classification of the numerical invariants of smooth surfaces of degree less than ten has been worked out. In this paper I will give an account of an attempt to give a classification of smooth surfaces of degree 10 in \(\mathbb{P}^4\), together with an overview of results concerning degrees less than 10. It contains a number of constructions. Often, many details of the proofs will be omitted here, they can be found in the author’s thesis [“On smooth surfaces of degree ten in the projective four space” (Univ. Oslo 1988)].For the entire collection see [Zbl 0824.00026]. Cited in 12 Documents MSC: 14J25 Special surfaces 14N05 Projective techniques in algebraic geometry 14M07 Low codimension problems in algebraic geometry Keywords:codimension 2; surface in projective 4-space PDFBibTeX XMLCite \textit{K. Ranestad}, Symp. Math. 32, 271--307 (1991; Zbl 0827.14023)