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pro vyhledávání: '"Shen, Mingmin"'
A de Rham-Betti class on a smooth projective variety $X$ over an algebraic extension $K$ of the rational numbers is a rational class in the Betti cohomology of the analytification of$X$ that descends to a class in the algebraic de Rham cohomology of
Externí odkaz:
http://arxiv.org/abs/2206.08618
Autor:
Shen, Mingmin
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 to the integral Hodge conjecture. One typical such counter-example is t
Externí odkaz:
http://arxiv.org/abs/1901.07091
The generalized Franchetta conjecture for hyper-K\"ahler varieties predicts that an algebraic cycle on the universal family of certain polarized hyper-K\"ahler varieties is fiberwise rationally equivalent to zero if and only if it vanishes in cohomol
Externí odkaz:
http://arxiv.org/abs/1708.02919
Autor:
Shen, Mingmin
We study the notion of a birational Chow-K\"unneth decomposition, which is essentially a decomposition of the integral birational motive of a variety. The existence of a birational Chow-K\"unneth decomposition is stably birationally invariant and thi
Externí odkaz:
http://arxiv.org/abs/1606.04762
Autor:
Shen, Mingmin
Publikováno v:
Geom. Topol. 23 (2019) 2861-2898
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 is universally generated by lines. Applications are mainly in cubic h
Externí odkaz:
http://arxiv.org/abs/1602.07331
Autor:
Shen, Mingmin
An error in Section 4 invalidates all the main results of the paper.
Comment: This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 4.2
Comment: This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 4.2
Externí odkaz:
http://arxiv.org/abs/1601.06308
Autor:
Shen, Mingmin, Vial, Charles
The Hilbert scheme $X^{[3]}$ of length-$3$ subschemes of a smooth projective variety $X$ is known to be smooth and projective. We investigate whether the property of having a multiplicative Chow-Kuenneth decomposition is stable under taking the Hilbe
Externí odkaz:
http://arxiv.org/abs/1503.00876
Autor:
Shen, Mingmin.
Thesis (Ph.D.)--Iowa State University, 2009.
Title from PDF title page (ProQuest website, viewed on March 30, 2010) Includes bibliography.
Title from PDF title page (ProQuest website, viewed on March 30, 2010) Includes bibliography.
Autor:
Shen, Mingmin, Vial, Charles
Using a codimension-$1$ algebraic cycle obtained from the Poincar\'e line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow ring $CH^
Externí odkaz:
http://arxiv.org/abs/1309.5965