25 citations · 76 across the 15 of their papers we have counts for
16 papers
De Rham-Betti classes with coefficients
Tobias Kreutz, Mingmin Shen, Charles Vial
Let and be algebraic extensions of the rational numbers inside the field of complex numbers. An -de Rham-Betti class on a smooth projective variety over is a cla…
The generalized Franchetta conjecture for some hyper-Kähler varieties, II
Lie Fu, Robert Laterveer, Charles Vial
We prove the generalized Franchetta conjecture for the locally complete family of hyper-Kähler eightfolds constructed by Lehn-Lehn-Sorger-van Straten (LLSS). As a corollary, we est…
Vanishing cycles under base change and the integral Hodge conjecture
Mingmin Shen
In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples t…
The generalized Franchetta conjecture for some hyper-Kähler varieties
Lie Fu, Robert Laterveer, Charles Vial +1
The generalized Franchetta conjecture for hyper-Kähler varieties predicts that an algebraic cycle on the universal family of certain polarized hyper-Kähler varieties is fiberwise r…
Birational Chow-Künneth decompositions
Mingmin Shen
We study the notion of a birational Chow-Künneth decomposition, which is essentially a decomposition of the integral birational motive of a variety. The existence of a birational C…
Rationality, universal generation and the integral Hodge conjecture
Mingmin Shen
We use the universal generation of algebraic cycles to relate (stable) rationality to the integral Hodge conjecture. We show that the Chow group of 1-cycles on a cubic hypersurface…