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- Creator:
- Sethuraman, Bharath, Jonov, Boyan, and Ghorpade, Sudhir
- Description:
- We consider the affine variety Zm,n2,2 of first-order jets over Zm,n2, where Zm,n2 is the classical determinantal variety given by the vanishing of all 2×2 minors of a generic m×n matrix. When 2<m≤n, this jet scheme Zm,n2,2 has two irreducible components: a trivial component, isomorphic to an affine space, and a nontrivial component that is the closure of the jets supported over the smooth locus of Zm,n2. This second component is referred to as the principal component of Zm,n2,2; it is, in fact, a cone and can also be regarded as a projective subvariety of P2mn−1. We prove that the degree of the principal component of Zm,n2,2 is the square of the degree of Zm,n2 and, more generally, the Hilbert series of the principal component of Zm,n2,2 is the square of the Hilbert series of Zm,n2. As an application, we compute the a-invariant of the principal component of Zm,n2,2 and show that the principal component of Zm,n2,2 is Gorenstein if and only if m=n.
- Resource Type:
- Article
- Identifier:
- 0030-8730
- Campus Tesim:
- Northridge

- Creator:
- Candel, Alberto and Alvarez Lopez, Jesus A.
- Description:
- A foliation is called Riemannian if its holonomy pseudogroup consists of local isometries for some Riemannian metric. By combining the work on Hilbert's fifth problem for local groups with our work on equicontinuous foliated spaces, we prove that, if a foliated space is strongly equicontinuous, locally connected and of finite dimension, has a dense leaf, and has holonomy pseudogroup whose closure is quasianalytic, then it is a Riemannian foliation.
- Resource Type:
- Article
- Identifier:
- 0030-8730
- Campus Tesim:
- Northridge

- Creator:
- Watkins, William E., Botta, Peter, and Pierce, Stephen
- Description:
- Let sln be the algebra of n × n matrices with zero trace and entries in a field with at least n elements. Let N be the set of nilpotent matrices. The main result in this paper is that the group of nonsingular linear transformations L on sln such that L(N) = N is generated by the inner automorphisms: X → S−1XS; the maps: X → aX, for a≠0; and the map: X → Xt that sends a matrix X to its transpose.
- Resource Type:
- Article
- Identifier:
- 0030-8730
- Campus Tesim:
- Northridge

- Creator:
- Fuller, Terry
- Description:
- Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over S2. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of an S2-bundle over S2, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes σ separating curves, we show that M is the relative minimalization of a Lefschetz fibration constructed as a 2-fold branched cover of ℂP2#(2σ + 1)ℂP2, branched over an embedded surface.
- Resource Type:
- Article
- Identifier:
- 0030-8730
- Campus Tesim:
- Northridge

- Creator:
- Dussan, Martha P. and Noronha, Maria H.
- Description:
- In this paper we study compact manifolds with 2-nonnegative Ricci operator, assuming that their Weyl operator satisfies certain conditions which generalize conformal flatness. As a consequence, we obtain that such manifolds are either locally symmetric or their Betti numbers between 2 and n − 2 vanish. We also study the topology of compact hypersurfaces with 2-nonnegative Ricci operator.
- Resource Type:
- Article
- Identifier:
- 0030-8730
- Campus Tesim:
- Northridge