The chain-level intersection product for PL pseudomanifolds revisited

2018 ◽  
Author(s):  
Greg Friedman
Keyword(s):  
Intersection Product ◽  
Level Intersection ◽  
Chain Level

Relations in the tautological ring derived from combinatorial classes and hyperelliptic fatgraphs

2008 ◽  
Vol 144 (2) ◽  
pp. 369-395
Author(s):  
ALEX JAMES BENE
Keyword(s):  
Moduli Space ◽  
Cell Decomposition ◽  
Integration Scheme ◽  
Weighted Sum ◽  
Closed Formula ◽  
Moduli Space Of Curves ◽  
Hodge Integrals ◽  
Tautological Ring ◽  
Level Intersection ◽  
Chain Level

AbstractA closed formula is obtained for the integral$\int_{\Hgbs^1}\kappa_{1}\psi^{2g-2}$of tautological classes over the locus of hyperelliptic Weier points in the moduli space of curves. As a corollary, a relation between Hodge integrals is obtained.The calculation utilizes the homeomorphism between the moduli space of curves$\M_{g,1}$and the combinatorial moduli space$\Mc_{g,1}$, a PL-orbifold whose cells are enumerated by fatgraphs. This cell decomposition can be used to naturally construct combinatorial PL-cycles$W_a\subset\Mc_{g,1}$whose homology classes are essentially the Poin duals of the Mumford–Morita–Miller classes κa. In this paper we construct another PL-cycle$\Hgc \subset \Mc_{g,1}$representing the locus of hyperelliptic Weier points and explicitly describe the chain level intersection of this cycle withW1. Using this description of$\Hgc\cap W_1$, the duality between Witten cyclesWaand the κaclasses, and the Kontsevich--Penner method of integration, scheme of integrating ε classes, the integral$\int_{\Hgbs^1}\kappa_{1}\psi^{2g-2}$is reduced to a weighted sum over graphs and is evaluated by the enumeration of trees.

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.

scholarly journals THE IMPACT OF THE COVID-19 PANDEMIC ON SUPPLY CHAINS IN THE AUTOMOTIVE INDUSTRY

2020 ◽  
Author(s):  
Goran Milovanovic ◽  
◽  
Tamara Stankovic ◽  
Keyword(s):  
Supply Chain ◽  
Supply Chains ◽  
Automotive Industry ◽  
Business Relationships ◽  
Automotive Supply Chain ◽  
Automotive Supply ◽  
The Impact ◽  
Insight Into ◽  
Chain Level

Health crises have an impact on supply chains, mainly by disrupting their regular activities. In this research, the authors have analyzed the impact that the Covid-19 pandemic has made on business relationships between supply chain partners in the automotive industry and their suppliers, which are mostly from territories where the initial outbreak of the SARS COV 2 virus occurred. The analysis shows that in some cases, there is a strong dependency between the pandemic and production levels. Being dependent prevents supply chains from maintaining stability and causes system vulnerabilities. The authors conclude their work with a thesis on the pronounced impact of the current pandemic on automotive supply chain activities. For the analysis to be complete, it is necessary to monitor changes in production levels further, since data for the current year still does not provide a realistic insight into all the consequences at the supply chain level.

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