arXiv subjects

Hiroki Minamide

Publications and source records attributed to Hiroki Minamide.

4 recordsLinked to original sources

arXiv2026

Finite-Sample Rigidity for Left-Translated Similarity Orbits and Off-Diagonal Quadratic Realizations

We study finite-sample rigidity for left translates of similarity orbits over commutative rings. Let $R$ be a commutative ring with $2\in R^\times$, and let $C\in\operatorname{Mat}_2(R)$ be cyclic. Given matrices $G_i=FK_i$, where $F\in\operatorname{GL}_2(R)$ is common and the underlying points $K_i$ lie in $\operatorname{Orb}(C)$, we determine when a finite translated sample has exactly the same multiplier ambiguity as the complete translated orbit. The key structural result is that the orbit differences span $\mathfrak{sl}_2(R)$, which yields a scalar description of the left stabilizer. We then give a determinantal saturation criterion, expressed directly in the matrices $G_i$, under which finite-sample consistency reduces to trace equations and one determinant condition. Off-diagonal quadratic operators on pairs of free rank-two modules realize the translated-orbit model exactly. Over fields we obtain sharp sample thresholds under the saturation criterion, and over finite fields we derive exact saturation probabilities for regular semisimple and nonzero nilpotent orbits. Torsion restrictions of elliptic isogenies provide a natural arithmetic realization of the rank-two module framework.

math.RA↗

arXiv2026

On the Adjacency spectra of alternating-oriented $n$-gonal staircase digraphs

For integers $n \ge 3$ and $r \ge 1$, let $\Gamma_{n,r}$ be the alternating-oriented digraph obtained by gluing $r$ directed $n$-cycles along a single edge in a staircase pattern, and let $A_{n,r}$ be its adjacency matrix. A canonical $n$-layer partition puts $A_{n,r}$ into an $n$-cyclic block form and isolates a cyclic product core $K_{n,r}$, so the nonzero spectrum of $A_{n,r}$ is obtained from that of $K_{n,r}$ by taking $n$th roots. We show that $K_{n,r}$ is totally nonnegative and irreducible, and hence its nonzero eigenvalues are real, positive, and simple. It follows that all nonzero eigenvalues of $A_{n,r}$ are simple and occur in $\exp(2\pi i/n)$-orbits, forming unions of regular $n$-gons in the complex plane. A one-step Schur complement yields a three-term recursion in $r$ for the characteristic polynomials $\Phi_{n,r} \in \mathbb{Z}[x]$. This determines both the multiplicity of the eigenvalue $0$ and the number of nonzero eigenvalues, and leads to a generating function with cubic denominator. Applying a Tran-type confinement theorem gives the uniform bound $\rho(A_{n,r}) \le (27/4)^{1/n}$ and the sharp limit $\displaystyle\lim_{r \to \infty} \rho(A_{n,r}) = (27/4)^{1/n}$ for each fixed $n$. Finally, specializing at $x=1$ relates $\Phi_{n,r}(1)$ to Padovan spiral numbers and yields a complete classification of rational nonzero eigenvalues.

math.CO↗

arXiv2012

Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions

Bridgeland stability condition is preserved under the Fourier-Mukai transform by its definition. We explain the relation with Gieseker stability. By studying the wall-crossing behavior, we reprove that the moduli spaces of stable sheaves on abelian surfaces are birationally equivalent, if the associated Mukai vectors are related by isometries of the Mukai lattice.

math.AG↗

arXiv2011

Some moduli spaces of Bridgeland's stability conditions

We shall study some moduli spaces of Bridgeland's semi-stable objects on abelian surfaces and K3 surfaces with Picard number 1. Under some conditions, we show that the moduli spaces are isomorphic to the moduli spaces of Gieseker semi-stable sheaves. We also study the ample cone of the moduli spaces.

math.AG↗