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We give re fined statements and modern proofs of Rosenlicht's re- sults about the canonical model C′ of an arbitrary complete integral curve C. Notably, we prove that C and C′ are birationally equivalent if and only if ...

This historical introduction is in two parts. The first is reprinted with permission from "A century of mathematics in America, Part II," Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been ...

Given a smooth family F/Y of geometrically irreducible surfaces, we study sequences of arbitrarily near T-points of F/Y; they generalize the traditional sequences of infinitely near points of a single smooth surface. We ...

We prove a projection formula, expressing a relative Buchsbaum–Rim multiplicity in terms of corresponding ones over a module-finite algebra of pure degree, generalizing an old formula for the ordinary (Samuel) multiplicity. ...

This article introduces, informally, the substance and the spirit of Grothendieck's theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger ...