55 citations · 93 across the 25 of their papers we have counts for
27 papers
Macaulay duality and its geometry
Steven L. Kleiman, Jan O. Kleppe
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is gener…
On the Quot scheme
Cristina Bertone, Steven L. Kleiman, Margherita Roggero
We consider the quot scheme of locally free quotients of with Hilbert po…
Two Formulas for the BR Multiplicity
Steven L. Kleiman
We prove a projection formula, expressing a relative Buchsbaum--Rim multiplicity in terms of corresponding ones over a module-finite algebra of pure degree, generalizing an old for…
The Picard Scheme
Steven L. Kleiman
This article introduces, informally, the substance and the spirit of Grothendieck's theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingeni…
Curve Counting à la Göttsche
Steven L. Kleiman
Let n_δbe the number of δ-nodal curves lying in a suitably ample complete linear system |L| and passing through appropriately many points on a smooth projective complex algebraic s…
On the Göttsche Threshold
Steven L. Kleiman, Vivek V. Shende, with an appendix by Ilya Tyomkin
For a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L an…