Introduction to intersection theory in algebraic geometry. Expository lectures from the CBMS regional conference, George Mason University, Fairfax, VA, USA, June 27–July 1, 1983. 3rd printing with corrections.

*(English)*Zbl 0913.14001
Regional Conference Series in Mathematics. 54. Providence, RI: American Mathematical Society (AMS). ix, 83 p. (1996).

These notes, written from the author’s expository lectures delivered at the CBMS regional conference at George Mason University (Fairfax, Virginia) in 1983, were first published fifteen years ago (1984), almost exactly at the same time when the author’s comprehensive monograph “Intersection theory” [cf.: W. Fulton, Intersection theory. Ergebn. Math. Grenzgeb., 3. Folge, Band 2, (1984; Zbl 0541.14005)] appeared. In fact, these notes provide a broad survey on many topics in both classical and modern intersection theory, the details of which had been elaborated in that brilliant monograph of W. Fulton’s. While the author’s nearly encyclopaedic book “Intersection theory” has quickly become the most important standard text on this subject, these notes have maintained their outstanding role as both a beautiful introduction and a masterly survey in this area of algebraic geometry. Now, in the present third printing of these notes, the author has taken the opportunity to correct some errors and misprints and, what is even more important, to add a section that up-dates the notes by pointing out some of the work that has been done in, and that is related to algebraic intersection theory since the first edition appeared. These additional remarks not only provide a (selective) up-dating of the bibliography, but guide the interested reader into various directions of the recent developments that the vivid area of intersection theory has undergone between 1983 and 1995.

Now as before, W. Fulton’s introductory notes are an excellent invitation to this subject, and a valuable spring of information for any mathematician interested in the methods of algebraic geometry in general.

Now as before, W. Fulton’s introductory notes are an excellent invitation to this subject, and a valuable spring of information for any mathematician interested in the methods of algebraic geometry in general.

Reviewer: W.Kleinert (Berlin)

##### MSC:

14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |

14-02 | Research exposition (monographs, survey articles) pertaining to algebraic geometry |

14C15 | (Equivariant) Chow groups and rings; motives |

14C40 | Riemann-Roch theorems |

14N10 | Enumerative problems (combinatorial problems) in algebraic geometry |

14M15 | Grassmannians, Schubert varieties, flag manifolds |

##### Keywords:

intersection theory; intersection multiplicities; algebraic cycles; rational equivalence; intersection rings; Chern classes; Segre classes; degeneracy loci; Schur polynomials; Riemann-Roch theorems; enumerative geometry
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\textit{W. Fulton}, Introduction to intersection theory in algebraic geometry. Expository lectures from the CBMS regional conference, George Mason University, Fairfax, VA, USA, June 27--July 1, 1983. 3rd printing with corrections. Providence, RI: American Mathematical Society (1996; Zbl 0913.14001)