Lazarsfeld, Robert Brill-Noether-Petri without degenerations. (English) Zbl 0608.14026 J. Differ. Geom. 23, 299-307 (1986). Petri’s conjecture was proved by D. Gieseker in Invent. Math. 66, 251–275 (1982; Zbl 0522.14015) by using a degeneration argument due to Griffiths and Harris. In the present paper it is proved that the general member of a complete linear system \(| C|\) on a K3 surface satisfies Petri’s condition provided every member in \(| C|\) is reduced and irreducible. This statement easily implies Petri’s conjecture. Its proof does not use degenerations; it is based on interpreting ”Petri’s condition” as a smoothness condition for a suitable map between manifolds. Reviewer: Alexandru Buium (Bucureşti) Cited in 8 ReviewsCited in 83 Documents MSC: 14C22 Picard groups 14J25 Special surfaces 14J28 \(K3\) surfaces and Enriques surfaces Keywords:Picard group; K3 surface; Petri’s condition Citations:Zbl 0522.14015 PDFBibTeX XMLCite \textit{R. Lazarsfeld}, J. Differ. Geom. 23, 299--307 (1986; Zbl 0608.14026) Full Text: DOI