Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.38906

On algebraic dynamics of birational automorphisms of Calabi-Yau manifolds and the universal Coxeter groups

Keiji Oguiso
View original source ↗Read source document ↗Export metadata ↓

Abstract

This is a continuation of our study of algebraic dymanics of birational automorphisms of complex Calabi-Yau manifolds in the view of primitivity and the existence of Zariski dense orbit. The universal Coxeter groups and their Coxeter elements also play important roles in our study.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Keiji Oguiso. 2026-09-30. On algebraic dynamics of birational automorphisms of Calabi-Yau manifolds and the universal Coxeter groups. https://arxiv.org/abs/2609.38906

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Voevodsky motives and motives with modulus in positive characteristic

Let $k$ be a perfect field of characteristic $p>0$. In this paper, without assuming resolution of singularities, we prove that the triangulated category of motives with modulus with rational coefficients is equivalent to Voevodsky's triangulated category of motives with rational coefficients $\MDM^\eff(k,\Q)\simeq \DM^\eff(k,\Q).$ Equivalently, after tensoring with $\Q$, the multiplicities of the modulus become invisible in the category of motives with modulus in positive characteristic.

math.AG↗
arXiv2026

Vanishing Theorems and Complex Structures on Non-Classical Flag Domains

Let $D=G_{\mathbb R}/V$ be a non-classical flag domain with $G_{\mathbb R}$ simple. We prove that every compact quotient of $D$ by a torsion-free discrete subgroup has no nonzero closed positive $(1,1)$-currents. Consequently, on any such quotient, every nontrivial holomorphic line bundle has no nonzero global sections, and a line bundle is pseudo-effective if and only if it is unitary flat. The proof combines a self-contained root-theoretic criterion with averaging of currents, without a homogeneity assumption on the line bundle. The same root criterion proves the Green--Griffiths--Kerr vanishing conjecture for locally homogeneous bundles induced by nontrivial irreducible representations of $V$ and gives an alternative proof of the Griffiths--Robles--Toledo bracket-generation lemma. For products of flag domains, we describe all closed positive $(1,1)$-currents on compact quotients by descent to the classical factors. If the lattice has dense joint projection to the classical subproduct, every such current is smooth. For non-classical domains of Hermitian type, we give an explicit second invariant complex structure whose compact quotients are projective, whereas the original quotients are not in Fujiki class $\mathcal C$. Finally, an explicit family on $SU(2,1)/H$ shows that topologically trivial holomorphic line bundles need not be homogeneous, even when their pullbacks to all rational curves are trivial.

math.AG↗
arXiv2026

The rationality problem for multinorm one tori

In this paper, we study the rationality problem for multinorm one tori, a natural generalization of norm one tori. For multinorm one tori that split over finite Galois extensions with nilpotent Galois group, we prove that stable rationality and retract rationality are equivalent, and give a criterion for the validity of the above two conditions. This generalizes the result of Endo (2011) on the rationality problem for norm one tori. To accomplish it, we introduce a generalization of character groups of multinorm one tori. Moreover, we establish systematic reduction methods originating in work of Endo (2001) for an investigation of the rationality problem for arbitrary multinorm one tori. In addition, we provide a new example for which the multinorm principle holds.

math.AG↗