scholarly journals A Tropical Intersection Product in Matroidal Fans

2013 ◽  
Vol 27 (1) ◽  
pp. 459-491 ◽  
Author(s):  
Kristin M. Shaw
Keyword(s):  
Intersection Product

scholarly journals Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type

2021 ◽  
Author(s):  
Lie Fu ◽  
Robert Laterveer ◽  
Charles Vial
Keyword(s):  
Projective Variety ◽  
Arbitrary Dimension ◽  
Smooth Projective Variety ◽  
The Other ◽  
Fano Variety ◽  
Fano Varieties ◽  
Intersection Product ◽  
Canonical Class ◽  
Main Input

AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Küchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Künneth decomposition, by establishing this for two families of Todorov surfaces.

scholarly journals ON THE CHOW RING OF CERTAIN LEHN–LEHN–SORGER–VAN STRATEN EIGHTFOLDS

2021 ◽  
pp. 1-24
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ROBERT LATERVEER
Keyword(s):  
Chow Group ◽  
Chow Ring ◽  
Similar Statement ◽  
Intersection Product ◽  
Finite Dimensional

Abstract We consider a 10-dimensional family of Lehn–Lehn–Sorger–van Straten hyperkähler eightfolds, which have a non-symplectic automorphism of order 3. Using the theory of finite-dimensional motives, we show that the action of this automorphism on the Chow group of 0-cycles is as predicted by the Bloch–Beilinson conjectures. We prove a similar statement for the anti-symplectic involution on varieties in this family. This has interesting consequences for the intersection product of the Chow ring of these varieties.

Properties of Arakelov's intersection product

1983 ◽  
pp. 138-145 ◽  
Author(s):  
G. Faltings
Keyword(s):  
Intersection Product

Pieri’S Formula Via Explicit Rational Equivalence

1997 ◽  
Vol 49 (6) ◽  
pp. 1281-1298 ◽  
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.

scholarly journals On the intersection product of analytic cycles

2000 ◽  
Vol 73 (2) ◽  
pp. 135-146 ◽  
Author(s):  
Sławomir Rams
Keyword(s):  
Intersection Product

scholarly journals Combinatorial duality and intersection product: A direct approach

2005 ◽  
Vol 57 (2) ◽  
pp. 273-292 ◽  
Author(s):  
Gottfried Barthel ◽  
Jean-Paul Brasselet ◽  
Karl-Heinz Fieseler ◽  
Ludger Kaup
Keyword(s):  
Direct Approach ◽  
Intersection Product

scholarly journals CHARACTERIZATION OF

2016 ◽  
Vol 224 (1) ◽  
pp. 1-9
Author(s):  
MERITXELL SÁEZ
Keyword(s):  
Geometric Characterization ◽  
Symmetric Product ◽  
Ample Divisor ◽  
Intersection Product ◽  
A Chain

In this paper a new geometric characterization of the $n$th symmetric product of a curve is given. Specifically, we assume that there exists a chain of smooth subvarieties $V_{i}$ of dimension $i$, such that $V_{i}$ is an ample divisor in $V_{i+1}$ and its intersection product with $V_{1}$ is one; that the Albanese dimension of $V_{2}$ is $2$ and the genus of $V_{1}$ is equal to the irregularity of the variety. We prove that in this case the variety is isomorphic to the symmetric product of a curve.

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