https://hdl.handle.net/1721.1/116034 2026-04-03T22:02:16Z 2026-04-03T22:02:16Z Altman, Allen Kleiman, Steven https://hdl.handle.net/1721.1/116075.2 2022-06-21T18:27:30Z 2021-04-11T00:00:00Z

A term of Commutative Algebra Altman, Allen; Kleiman, Steven There is no shortage of books on Commutative Algebra, but the present book is different. Most books are monographs, with extensive coverage. But there is one notable exception: Atiyah and Macdonald's 1969 classic. It is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics and exercises. So it has remained popular. However, its age and flaws do show, including many unsolved exercises. So there is need for an updated and improved version, which includes solutions to all their exercises and to many more. The present book aims to be that version.

2021-04-11T00:00:00Z Altman, Allen Kleiman, Steven https://hdl.handle.net/1721.1/116075 2021-08-26T16:58:56Z 2013-05-04T00:00:00Z

A term of Commutative Algebra Altman, Allen; Kleiman, Steven There is no shortage of books on Commutative Algebra, but the present book is different. Most books are monographs, with extensive coverage. But there is one notable exception: Atiyah and Macdonald's 1969 classic. It is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics and exercises. So it has remained popular. However, its age and flaws do show, including many unsolved exercises. So there is need for an updated and improved version, which includes solutions to all their exercises and to many more. The present book aims to be that version. Second, enlarged edition

2013-05-04T00:00:00Z Kleiman, Steven L. https://hdl.handle.net/1721.1/107775 2022-10-02T00:39:38Z 2016-07-01T00:00:00Z

Two formulas for the BR multiplicity Kleiman, Steven L. 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. Our proof is simple in spirit: after the multiplicities are expressed as sums of intersection numbers, the desired formula results from two projection formulas, one for cycles and another for Chern classes. Similarly, but without using any projection formula, we prove an expansion formula, generalizing the additivity formula for the ordinary multiplicity, a case of the associativity formula.

2016-07-01T00:00:00Z Kleiman, Steven L. https://hdl.handle.net/1721.1/87083 2022-09-28T19:30:47Z 2013-09-01T00:00:00Z

The Picard Scheme Kleiman, Steven L. 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 historical record.

2013-09-01T00:00:00Z Kleiman, Steven L. Piene, Ragni Tyomkin, Ilya https://hdl.handle.net/1721.1/71149 2022-09-26T13:12:17Z 2011-09-01T00:00:00Z

Enriques diagrams, arbitrarily near points, and Hilbert schemes Kleiman, Steven L.; Piene, Ragni; Tyomkin, Ilya 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 distinguish a special sort of these new sequences, the strict sequences. To each strict sequence, we associate an ordered unweighted Enriques diagram. We prove that the various sequences with a fixed diagram form a functor, and we represent it by a smooth Y-scheme. We equip this Y-scheme with a free action of the automorphism group of the diagram. We equip the diagram with weights, take the subgroup of those automorphisms preserving the weights, and form the corresponding quotient scheme. Our main theorem constructs a canonical universally injective map from this quotient scheme to the Hilbert scheme of F/Y; further, this map is an embedding in characteristic 0. However, in every positive characteristic, we give an example, in Appendix B, where the map is purely inseparable.

2011-09-01T00:00:00Z Kleiman, Steven L. https://hdl.handle.net/1721.1/69980 2022-09-26T17:00:12Z 2008-06-01T00:00:00Z

The Development of Intersection Homology Theory Kleiman, Steven L. 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 made to the original text. In particular, Section 8 is followed by the original list of references. However, the text has been supplemented by a series of endnotes, collected in the new Section 9 and followed by a second list of references. If a citation is made to the first list, then its reference number is simply enclosed in brackets -- for example, [36]. However, if a citation is made to the second list, then its number is followed by an 'S' -- for example, [36S]. Further, if a subject in the reprint is elaborated on in an endnote, then the subject is flagged in the margin by the number of the corresponding endnote, and the endnote includes in its heading, between parentheses, the page number or numbers on which the subject appears in the reprint below. Finally, all cross-references appear as hypertext links in the dvi and pdf copies. 58 pages, hypertext links added; appeared in Part 3 of the special issue of Pure and Applied Mathematics Quarterly in honor of Robert MacPherson. However, the flags in the margin were unfortunately (and inexplicably) omitted from the published version.

2008-06-01T00:00:00Z Kleiman, Steven L. Vidal Martins, Renato https://hdl.handle.net/1721.1/62837 2022-09-29T15:31:03Z 2009-04-01T00:00:00Z

The Canonical Model of a Singular Curve Kleiman, Steven L.; Vidal Martins, Renato 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 C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equal to the blowup of C with respect to the canonical sheaf [omega]. We also prove some new results: we determine just when C′ is rational normal, arithmetically normal, projectively normal, and linearly normal.

2009-04-01T00:00:00Z