Rational Equivalence | ScienceGate

Rational equivalence and Phantom map out of a loop space, II

Journal of Mathematics of Kyoto University ◽

10.1215/kjm/1250283085 ◽

2004 ◽

Vol 44 (3) ◽

pp. 595-601 ◽

Cited By ~ 1

Author(s):

Kouyemon Iriye

Keyword(s):

Loop Space ◽

Rational Equivalence

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Rational equivalence of a form to a sum of $p$th powers

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1938-1501968-x ◽

1938 ◽

Vol 44 (2) ◽

pp. 219-219

Author(s):

Rufus Oldenburger

Keyword(s):

Rational Equivalence

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Invariants of rational equivalence

Siberian Mathematical Journal ◽

10.1007/bf02674605 ◽

2000 ◽

Vol 41 (2) ◽

pp. 357-361 ◽

Cited By ~ 3

Author(s):

A. G. Pinus

Keyword(s):

Rational Equivalence

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Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady

Recent Advances in Algebraic Geometry ◽

10.1017/cbo9781107416000.021 ◽

2015 ◽

pp. 422-436 ◽

Cited By ~ 4

Author(s):

C. Voisin

Keyword(s):

K3 Surfaces ◽

Rational Equivalence

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Pieri’S Formula Via Explicit Rational Equivalence

Canadian Journal of Mathematics ◽

10.4153/cjm-1997-063-7 ◽

1997 ◽

Vol 49 (6) ◽

pp. 1281-1298 ◽

Cited By ~ 7

Author(s):

Frank Sottile

Keyword(s):

Combinatorial Proof ◽

Geometric Proof ◽

Intersection Product ◽

Rational Equivalence ◽

Schubert Cycles

AbstractPieri’s formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a Schubert cycle with a special Schubert cycle. The geometry of these rational equivalences indicates a link to a combinatorial proof of Pieri’s formula using Schensted insertion.

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On Rational Equivalence in Tropical Geometry

Canadian Journal of Mathematics ◽

10.4153/cjm-2015-036-0 ◽

2016 ◽

Vol 68 (2) ◽

pp. 241-257 ◽

Cited By ~ 5

Author(s):

Lars Allermann ◽

Simon Hampe ◽

Johannes Rau

Keyword(s):

Tropical Geometry ◽

Chow Groups ◽

Independent Interest ◽

Main Step ◽

Rational Equivalence ◽

Basic Properties ◽

Boundary Points ◽

Intersection Ring ◽

Tropical Varieties

AbstractThis article discusses the concept of rational equivalence in tropical geometry (and replaces an older, imperfect version). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties. We then compute the “bounded” Chow groups of Rn by showing that they are isomorphic to the group of fan cycles. The main step in the proof is of independent interest. We show that every tropical cycle in Rn is a sum of (translated) fan cycles. This also proves that the intersection ring of tropical cycles is generated in codimension 1 (by hypersurfaces).

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