arXiv subjects

Charles H. Walter

Publications and source records attributed to Charles H. Walter.

4 recordsLinked to original sources

arXiv1994

Pfaffian Subschemes

A subscheme $X\subset \Bbb P^{n+3}$ of codimension $3$ is {\em Pfaffian} if it is the degeneracy locus of a skew-symmetric map $f:\cal{E}\spcheck(-t) @>>> \cal{E}$ with $\cal{E}$ a locally free sheaf of odd rank on $\Bbb P^{n+3}$. It is shown that a codimension $3$ subscheme $X\subset\Bbb P^{n+3}$ is Pfaffian if and only if it is locally Gorenstein, subcanonical (i.e.\ $ω_X\cong\cal O_X(l)$ for some integer $l$), and the following parity condition holds: if $n\equiv 0\pmod{4}$ and $l$ is even, then $χ(\cal O_X (l/2))$ is also even. The paper includes a modern version of the Horrocks correspondence, stated in the language of derived categories. A local analogue of the main theorem is also proved.

alg-geom↗

arXiv1994

On Chow Rings of Fine Moduli Spaces of Modules

Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal $S$-module on $M$. This result is then applied to the varieties $G_T$ parametrizing homogeneous ideals of $k[x,y]$ of Hilbert function $T$, to moduli spaces of representations of quivers, and finally to moduli spaces of sheaves on ${\Bbb P}^2$, reinterpreting a result of Ellingsrud and Strømme.

alg-geom↗

arXiv1993

On the Harder-Narasimhan Filtration for Coherent Sheaves on P2: I

Let E be a torsion-free sheaf on P2. We give an effective method which uses the Hilbert function of E to construct a weak version of the Harder-Narasimhan filtration of a torsion-free sheaf on P2 subject only to the condition that E be sufficiently general among sheaves with that Hilbert function. This algorithm uses on a generalization of Davis' decomposition lemma to higher rank.

alg-geom↗

arXiv1993

Components of the Stack of Torsion-Free Sheaves of Rank 2 on Ruled Surfaces

Let S be a ruled surface without sections of negative self-intersection. We classify the irreducible components of the moduli stack of torsion-free sheaves of rank 2 sheaves on S. We also classify the irreducible components of the Brill-Noether loci in Hilb^N(P1xP1) given by W_N^0(D)={[X] | h^1(I_X(D)) >= 1 } for D an effective divisor class. Our methods are also applicable to P2 giving new proofs of theorems of Stromme (slightly extended) and Coppo.

alg-geom↗