JP Journal of Algebra, Number Theory and Applications
Volume 7, Issue 1, Pages 131 - 151
(February 2007)
|
|
AN EXTENSION OF THE THOM-PORTEOUS FORMULA TO A CERTAIN CLASS OF COHERENT SHEAVES
Travis Lee (U. S. A.)
|
Abstract: The goal is a theorem which allows computations analogous to the Thom-Porteous formula for a morphism of coherent sheaves, which are not vector bundles, over a scheme X. In particular if is the subset where either E or F is not a vector bundle, then the goal is to find a class supported on the set
S. Diaz has one method for accomplishing this goal: find a blow up such that the double dual of the pullbacks of E and F, namely and are vector bundles over Hence over there is a morphism of vector bundles For an appropriate choice of k, apply the Thom-Porteous formula to compute the fundamental class of Then is a class supported on in X. To derive a formula from this construction it suffices to express the Chern classes of and in terms of known information about E and F. A formula for these Chern classes is derived for E and F belonging to a certain class of coherent sheaves. |
Keywords and phrases: Thom-Porteous formula, coherent sheaves, intersection theory, Chern class. |
|
Number of Downloads: 460 | Number of Views: 905 |
|