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Equivariant Intersection Theory
 Invent. Math
, 1996
"... this paper is to develop an equivariant intersection theory for actions of linear algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology groups which have all the functorial properties of ordin ..."
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Cited by 161 (18 self)
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this paper is to develop an equivariant intersection theory for actions of linear algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology groups which have all the functorial properties
Intersection theory on the . . .
, 2008
"... We define a new family of open GromovWitten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an antisymplectic involution and ..."
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We define a new family of open GromovWitten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an antisymplectic involution
INTERSECTION THEORY
"... ABSTRACT. I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincare ́ dual of a submanifold 4 3. Smooth cycles and their intersections 8 ..."
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ABSTRACT. I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincare ́ dual of a submanifold 4 3. Smooth cycles and their intersections 8
Intersection Theory
"... Cycles. Let X be a nonsingular projective variety over an algebraically closed field C. A kcycle on X is a finite formal sum ni[Zi] where each Zi is a closed subvariety of dimension k. Pushforward. Suppose that f: X → Y is a morphism of projective smooth varieties. Let Z ⊂ X be a kdimensional clos ..."
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Cycles. Let X be a nonsingular projective variety over an algebraically closed field C. A kcycle on X is a finite formal sum ni[Zi] where each Zi is a closed subvariety of dimension k. Pushforward. Suppose that f: X → Y is a morphism of projective smooth varieties. Let Z ⊂ X be a kdimensional closed subvariety. We define f∗[Z] to be 0 if dim(f(Z)) < k and d · [f(Z)] if dim(f(Z)) = k where d = [C(Z) : C(f(Z))]. Let α = ni[Zi] be a kcycle on Y. The pushforward of α is the sum f∗α = nif∗[Zi] where each f∗[Zi] is defined as above. Cycle associated to closed subscheme. Suppose that X is a nonsingular projective variety and that Z ⊂ X is a closed subscheme with dim(Z) ≤ k. Let Zi be the irreducible components of Z of dimension k and let ni be the length of the local ring of Z at the generic point of Zi. We define the kcycle associated to Z to be the kcycle [Z]k = ni[Zi]. Cycle associated to a coherent sheaf. Suppose that X is a nonsingular projective variety and that F
Intersection Theory
"... Cycles. Let X be a nonsingular projective variety over an algebraically closed field C. A kcycle on X is a finite formal sum ∑ ni[Zi] where each Zi is a closed subvariety of dimension k. Pushforward. Suppose that f: X → Y is a morphism of projective smooth varieties. Let Z ⊂ X be a kdimensional cl ..."
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Cycles. Let X be a nonsingular projective variety over an algebraically closed field C. A kcycle on X is a finite formal sum ∑ ni[Zi] where each Zi is a closed subvariety of dimension k. Pushforward. Suppose that f: X → Y is a morphism of projective smooth varieties. Let Z ⊂ X be a kdimensional closed subvariety. We define f∗[Z] to be 0 if dim(f(Z)) < k and d · [f(Z)] if dim(f(Z)) = k where d = [C(Z) : C(f(Z))]. Let α = ∑ ni[Zi] be a kcycle on Y. The pushforward of α is the sum f∗α = ∑ nif∗[Zi] where each f∗[Zi] is defined as above. Cycle associated to closed subscheme. Suppose that X is a nonsingular projective variety and that Z ⊂ X is a closed subscheme with dim(Z) ≤ k. Let Zi be the irreducible components of Z of dimension k and let ni be the length of the local ring of Z at the generic point of Zi. We define the kcycle associated to Z to be the kcycle [Z]k = ∑ ni[Zi]. Cycle associated to a coherent sheaf. Suppose that X is a nonsingular projective variety and that F is a coherent OXmodule on X with dim(Supp(F)) ≤ k. Let Zi be the irreducible components of Supp(F) of dimension k and let ni be the length of the stalk of F at the generic point of Zi. We define the kcycle associated to F to be the kcycle [F]k = ∑ ni[Zi]. Note that, if dim(Z) ≤ k, then [Z]k = [OZ]k.
THE FIBERWISE INTERSECTION THEORY
"... Abstract. We define a bordism invariant for the fiberwise intersection theory. Under some certain conditions, this invariant is an obstruction for the theory. 1. ..."
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Abstract. We define a bordism invariant for the fiberwise intersection theory. Under some certain conditions, this invariant is an obstruction for the theory. 1.
Homotopical intersection theory
, 2009
"... Abstract. We give a new approach to intersection theory. Our “cycles ” are closed manifolds mapping into compact manifolds and our “intersections ” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjuncti ..."
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Cited by 10 (1 self)
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Abstract. We give a new approach to intersection theory. Our “cycles ” are closed manifolds mapping into compact manifolds and our “intersections ” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking
Equivariant cohomology and equivariant intersection theory
, 2008
"... This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain ..."
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Cited by 68 (4 self)
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This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain
Intersection Theory on Spherical Varieties
 PROCEEDINGS OF THE HERBRAND SYMPOSION., NORTHHOLLAND
, 1994
"... ..."
Intersection theory, integrable hierarchies and topological field theory
, 1992
"... In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological field theory. We focus in particular on the question why matrix integrals of the type considered by Kontsevic ..."
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Cited by 118 (5 self)
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In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological field theory. We focus in particular on the question why matrix integrals of the type considered
Results 1  10
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354,636