A correspondence between Hilbert polynomials and Chern polynomials over projective spaces

Chan, C.-Y. Jean

Illinois J. Math., Tome 48 (2004) no. 3, p. 451-462 / Harvested from Project Euclid

Résumé

We construct a map $\zeta$ from $\K(\mathbb P^d)$ to $(\mathbb Z[x]/x^{d+1})^{\times} \times \mathbb Z$, where $(\mathbb Z[x]/x^{d+1})^{\times}$ is a multiplicative Abelian group with identity $1$, and show that $\zeta$ induces an isomorphism between $\K(\mathbb P^d)$ and its image. This is inspired by a correspondence between Chern and Hilbert polynomials stated in Eisenbud~\cite[Exercise~19.18]{E}. The equivalence of these two polynomials over $\mathbb P^d$ is discussed in this paper.

Publié le : 2004-04-15
Classification: 14C35, 14C17, 19E08

@article{1258138391,
     author = {Chan, C.-Y. Jean},
     title = {A correspondence between Hilbert polynomials and Chern polynomials over projective spaces},
     journal = {Illinois J. Math.},
     volume = {48},
     number = {3},
     year = {2004},
     pages = { 451-462},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138391}
}

Chan, C.-Y. Jean. A correspondence between Hilbert polynomials and Chern polynomials over projective spaces. Illinois J. Math., Tome 48 (2004) no. 3, pp.  451-462. http://gdmltest.u-ga.fr/item/1258138391/