Related papers: Real intersection homology II: A local duality obs…
We prove a Lefschetz duality result for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a "collared neighborhood of their boundary". Our duality does not need this assumption…
We prove that the automorphism group of a general complete intersection $X$ in a projective space is trivial with a few well-understood exceptions. We also prove that the automorphism group of a complete intersection $X$ acts on the…
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…
Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.
Classically, the projective duality between joins of varieties and the intersections of varieties only holds in good cases. In this paper, we show that categorically, the duality between joins and intersections holds in the framework of…
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
This paper defines new intersection homology groups. The basic idea is this. Ordinary homology is locally trivial. Intersection homology is not. It may have significant local cycles. A local-global cycle is defined to be a family of such…
We define a variant of intersection space theory that applies to many compact complex and real analytic spaces $X$, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to…
We present a definition of intersection homology for real algebraic varieties that is analogous to Goresky and MacPherson's original definition of intersection homology for complex varieties.
We provide a novel proof of the homological excess intersection formula for local complete intersections. The novelty is that the proof makes use of global morphisms comparing the intersections to a self intersection.
Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.
Intersection homology with coefficients in a field restores Poincar\'e duality for some spaces with singularities, as pseudomanifolds. But, with coefficients in a ring, the behaviours of manifolds and pseudomanifolds are different. This…
We discuss duality pairings on integral \'etale motivic cohomology groups of regular and proper schemes over algebraically closed fields, local fields, finite fields, and arithmetic schemes.
In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant theoretic quotients for which semistability is not necessarily the…
We review some facts about various T-dualities and sigma models on group manifolds, with particular emphasis on supersymmetry. We point out some of the problems in reconciling Poisson-Lie duality with the bi-hermitean geometry of N=2…
Continuing from part (I), we develop properties of real intersection theory that turns out to be an extension of the well-established theory in algebraic geometry.
We compare the sheaf-theoretic and singular chain versions of Poincare duality for intersection homology, showing that they are isomorphic via naturally defined maps. Similarly, we demonstrate the existence of canonical isomorphisms between…
Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…
We give a non-constructive proof that fusion rings attached to a simple complex Lie algebra of rank 2 are complete intersections.
We prove the Lefschetz duality for intersection (co)homology in the framework of $\partial$-pesudomanifolds. We work with general perversities and without restriction on the coefficient ring.