Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The MacRae invariant and the first local Chern character

Author: Paul Roberts
Journal: Trans. Amer. Math. Soc. 300 (1987), 583-591
MSC: Primary 14C17; Secondary 13D15, 13D25, 14C35
MathSciNet review: 876467
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The first local Chern character of a bounded complex of locally free sheaves on a scheme $ Y$ is given by intersection with a Cartier divisor. In the case of the resolution of a module of finite projective dimension, this is the invariant defined by MacRae.

References [Enhancements On Off] (What's this?)

  • [1] Mario Borelli, Some results on ampleness and divisorial schemes, Pacific J. Math. 23 (1967), 217–227. MR 0219545
  • [2] Sankar P. Dutta, M. Hochster, and J. E. McLaughlin, Modules of finite projective dimension with negative intersection multiplicities, Invent. Math. 79 (1985), no. 2, 253–291. MR 778127, 10.1007/BF01388973
  • [3] Hans-Bjørn Foxby, The MacRae invariant, Commutative algebra: Durham 1981 (Durham, 1981) London Math. Soc. Lecture Note Ser., vol. 72, Cambridge Univ. Press, Cambridge, 1982, pp. 121–128. MR 693631
  • [4] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • [5] A Grothendieck and J. Dieudonne, Éléments de géométrie algébrique, Inst. Hautes Études Sci. Publ. Math. No. 4 (1960).
  • [6] R. E. MacRae, On an application of the Fitting invariants, J. Algebra 2 (1965), 153–169. MR 0178038
  • [7] Paul C. Roberts, Local Chern characters and intersection multiplicities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 389–400. MR 927989
  • [8] B. Iversen, On determinants of complexes, Aarhus Univ. Preprint Series no. 4, 1979/80.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14C17, 13D15, 13D25, 14C35

Retrieve articles in all journals with MSC: 14C17, 13D15, 13D25, 14C35

Additional Information

Article copyright: © Copyright 1987 American Mathematical Society