Details

Marco Maggesi ^[a] and Gabriele Vezzosi ^[a]

Some elementary remarks on lci algebraic cycles

Pages: 365-372
Received: 3 November 2018
Accepted: 7 December 2018
Mathematics Subject Classification (2010): 19-XX, 14CXX.
Keywords: K-theory, lci algebraic cycles.
Authors address:
[a]: University of Florence, Florence, Italy

Abstract: In this short note, we collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational equivalence. We also add a few observations on these representation problems that we were not able to locate in the literature.

References

[Fu]: W. Fulton, Intersection theory, 2nd ed., Springer-Verlag, Berlin, 1998. MR1644323
[Ha1]: R. Hartshorne, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York-Heidelberg, 1977. MR0463157
[Ha2]: R. Hartshorne, Deformation theory, Grad. Texts in Math., 257, Springer, New York, 2010. MR2583634
[Ha3]: R. Hartshorne, Topological conditions for smoothing algebraic singularities, Topology 13 (1974), 241–253. MR0349677
[Ha-Hi]: R. Hartshorne and A. Hirschowitz, Smoothing algebraic space curves, Algebraic Geometry, Sitges (Barcelona), 1983, Lecture Notes in Math., 1124, Springer, Berlin, 1985, 98–131. MR0805332
[HRT]: R. Hartshorne, E. Rees and E. Thomas, Nonsmoothing of algebraic cycles on Grassmann varieties, Bull. Amer. Math. Soc. 80 (1974), 847–851. MR0357402
[Hi]: H. Hironaka, Smoothing of algebraic cycles of small dimension, Amer. J. Math. 90 (1968), 1–54. MR0224611
[Kl]: S. L. Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Inst. Hautes études Sci. Publ. Math. 36 (1969), 281–297. MR0265371