Decency and Rigidity over Hypersurfaces
نویسنده
چکیده
We study two properties of modules over an equicharacteristic or unramified local hypersurface R: decency and rigidity. We show that the vanishing of Hochster’s function θ(M,N), known to imply decent intersection, also implies rigidity. We investigate the vanishing of θ(M,N) to obtain new results about decency and rigidity over hypersurfaces. We employ a mixture of techniques from Commutative Algebra and Intersection Theory of algebraic cycles.
منابع مشابه
Linear Weingarten hypersurfaces in a unit sphere
In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].
متن کاملSome Observations on Local and Projective Hypersurfaces
Let R be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules (M, N) over R we study applications of rigidity of Tor(M, N), based on ideas by Huneke, Wiegand and Jorgensen. We then focus on the hypersurfaces with isolated singularity and even dimension, and show that modules over such rings behave very much like those over regular local rings. Connecti...
متن کاملSpacelike hypersurfaces in de Sitter space
In this paper, we study the close spacelike hypersurfaces in de Sitter space. Using Bonnet-Myer’s theorem, we prove a rigidity theorem for spacelike hypersurfaces without the constancy condition on the mean curvature or the scalar curvature. M.S.C. 2010: 53C40, 53B30.
متن کاملSphere Rigidity in the Euclidean Space Julien
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almostumbilic hypersurfaces and new characterizations of geodesic spheres.
متن کامل