Motivation for Hodge cycles

By D. Arapura. 2005

63 citations recorded by the source corpus.

Given two smooth projective varieties X and Y, X is defined to motivate Y if the motive of Y is contained in the tensor category generated by X. Some techniques are given for checking this condition. It is shown that in a number of cases moduli spaces of sheaves over curves or surfaces are motivated by the underlying curve or surface. This is used to check the Hodge and related conjectures for some of these examples.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/371dfaddcb7ec0ad3b420436083256e9948b7258

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. M. Shen
2. Robert Laterveer
3. Charles Vial
4. E. Markman
5. Franccois Charles
6. L. Fu
7. Giovanni Mongardi

In Geometry and Topology

1. M. Shen
2. L. Fu
3. Franccois Charles
4. Charles Vial
5. Robert Laterveer
6. E. Markman
7. D. Huybrechts
8. Giovanni Mongardi

In Mathematical Physics

1. M. Shen
2. L. Fu
3. Franccois Charles
4. Charles Vial
5. Robert Laterveer
6. E. Markman
7. D. Huybrechts
8. C. Liedtke

Citations in the corpus

• Algebraic cycles and fibrations (2012, methodology): “Note that the second point of Theorem 7.1 does not seem to follow directly from the method of Arapura [1], since under our assumptions, it is not clear that the middle cohomology group of X is motivated by the cohomology of surfaces.”
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, result): “In particular, this implies that V satisfies the standard conjectures, by Arapura [Ara06, Lem.”
• The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces (2010, background): “morphic to the Chow ring A∗(X), see [K2]. Varieties with the latter property include flag varieties, and smooth projective moduli spaces of sheaves on rational Poisson surfaces [ES, Ma2]. In the paper [Ar], Arapura proves that the Lefschetz standard conjecture holds for uniruled threefolds, uniration”
• PROJECTORS ON THE INTERMEDIATE ALGEBRAIC JACOBIANS (2009, background): “to a Fano fourfold) has a Chow-Ku¨nneth decomposition and satisfies the motivic Lefschetz conjecture. Proof. A rationally connected smooth projective fourfold Xsatisfies CH0(X) = Q. Remark 4.9. Arapura [3] proved the Lefschetz standard conjecture for unirational fourfolds. He does so by proving that a”