arXiv subjects

Chenyu Bai

Publications and source records attributed to Chenyu Bai.

6 recordsLinked to original sources

arXiv2026

Cs$_4$Cr$_7$Te$_{10}$: Interwoven Reconstructed Archimedean and Kagome Lattices with a Possible Phase Transition near 130 K

Chromium-based materials with complex lattice geometries provide an important platform for investigating correlated electronic and magnetic states. However, Cr-based compounds with unusual crystal geometries are still rarely reported. Here, we report a new Cr-based compound, Cs$_4$Cr$_7$Te$_{10}$, featuring interwoven Cr and Te sublattices that can be viewed as reconstructed networks derived from Archimedean (3.4.6.4) tiling and the kagome lattice, respectively. Transport measurements reveal the semiconducting nature in Cs$_4$Cr$_7$Te$_{10}$. Magnetization measurements show a weak anisotropy between H//b and H//ac planes, and uncover an anomaly near 130 K that is insensitive to the applied magnetic fields. Specific-heat measurements further confirm this transition, indicating its bulk thermodynamic nature. The associated entropy change is as small as 0.41 J mol^-1 K^-1, ruling out a structural phase transition and pointing to a possible electronic and/or magnetic phase transition. These results provide a new route for designing complex crystal geometries and exploring their associated emergent phenomena.

cond-mat.mtrl-sci↗

arXiv2024

Hodge theory, algebraic cycles of hyper-Kähler manifolds

This thesis is devoted to the study of algebraic cycles in projective hyper-Kähler manifolds and strict Calabi-Yau manifolds. It contributes to the understanding of Beauville's and Voisin's conjectures on the Chow rings of projective hyper-Kähler manifolds and strict Calabi-Yau manifolds. It also studies some birational invariants of projective hyper-Kähler manifolds.

math.AG↗

arXiv2024

On the geometry of the higher dimensional Voisin maps

Voisin constructed self-rational maps of Calabi-Yau manifolds obtained as varieties of $r$-planes in cubic hypersurfaces of adequate dimension. This map has been thoroughly studied in the case $r=1$, which is the Beauville-Donagi case. In this paper, we compute the action of $Ψ$ on holomorphic forms for any $r$. For $r=2$, we compute the action of $Ψ$ on the Chow group of $0$-cycles, and confirm that it is as expected from the generalized Bloch conjecture.

math.AG↗

arXiv2022

On some birational invariants of hyper-Kähler manifolds

We study in this article three birational invariants of projective hyper-Kähler manifolds: the degree of irrationality, the fibering gonality and the fibering genus. We first improve the lower bound in a recent result of Voisin saying that the fibering genus of a Mumford--Tate very general projective hyper-Kähler manifold is bounded from below by a constant depending on its dimension and the second Betti number. We also study the relations between these birational invariants for projective K3 surfaces of Picard number 1 and study the asymptotic behaviors of their degree of irrationality and fibering genus.

math.AG↗

arXiv2022

On Abel-Jacobi Maps of Lagrangian Families

We study in this article the cohomological properties of Lagrangian families on projective hyper-Kähler manifolds. First, we give a criterion for the vanishing of Abel-Jacobi maps of Lagrangian families. Using this criterion, we show that under a natural condition, if the variation of Hodge structures on the degree $1$ cohomomology of the fibers of the Lagrangian family is maximal, its Abel-Jacobi map is trivial. We also construct Lagrangian families on generalized Kummer varieties whose Abel-Jacobi map is not trivial, showing that our criterion is optimal.

math.AG↗

arXiv2018

On Fano complete intersections in rational homogeneous varieties

Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if $X = \cap_{i=1}^r D_i \subset G/P$ is a general complete intersection of $r$ ample divisors such that $K_{G/P}^* \otimes \mathcal{O}_{G/P}(-\sum_i D_i)$ is ample, then $X$ is Fano. We first classify these Fano complete intersections which are locally rigid. It turns out that most of them are hyperplane sections. We then classify general hyperplane sections which are quasi-homogeneous.

math.AG↗