Akihiro Koide

Complete Defectivity and Simplex-Range Rational Identifiability for Homoscedastic Gaussian Moment Varieties

This work gives a complete dimension and defectivity classification for homoscedastic Gaussian moment varieties over an algebraically closed field of characteristic zero. It proves that these varieties have the expected dimension for every moment order at least four and combines...

Complete Defectivity and Simplex-Range Rational Identifiability for Homoscedastic Gaussian Moment Varieties

This work gives a complete dimension and defectivity classification for homoscedastic Gaussian moment varieties over an algebraically closed field of characteristic zero. It proves that these varieties have the expected dimension for every moment order at least four and combines...

A Certified Negative Interval for the Ninth Derivative Laguerre Quantity of the Riemann Xi Kernel

This revised preprint studies the derivative Laguerre quantities associated with the Jacobi theta kernel in the Fourier representation of the Riemann xi-function. It gives exact rational certificates showing that the ninth quantity is negative throughout a nontrivial interval aro...

Nonnegative Multiweight Smith Profiles and Contracted Strata of Shared-Socle Jordan Degenerations

This article studies one-parameter degenerations of chains of nilpotent Jordan blocks joined along their socle vectors. It gives a complete Smith-normal-form description of the associated self-extension torsion for arbitrary chain length and all nonnegative edge valuations. The r...

Nonnegative Multiweight Smith Profiles and Contracted Strata of Shared-Socle Jordan Degenerations

This article studies one-parameter degenerations of chains of nilpotent Jordan blocks joined along their socle vectors. It gives a complete Smith-normal-form description of the associated self-extension torsion for arbitrary chain length and all nonnegative edge valuations. The r...

A Certified Negative Interval for the Ninth Derivative Laguerre Quantity of the Riemann Xi Kernel

This revised preprint studies the derivative Laguerre quantities associated with the Jacobi theta kernel in the Fourier representation of the Riemann xi-function. It gives exact rational certificates showing that the ninth quantity is negative throughout a nontrivial interval aro...

Full-Secant Singularities of Veronese Varieties with Reduced Singleton Border VSP

This paper gives a negative answer to Question 35 of Furukawa and Han by constructing an explicit family of singular points on full secant varieties of Veronese varieties. The construction works for every border rank of at least six, every compatible ambient dimension, and every...

Counterexamples to Park's Coherent-Sheaf Conjecture and a Bounded-Edge MCM Extension

This paper disproves Park’s conjectural extension of asymptotic syzygy nonvanishing from line bundles to arbitrary coherent sheaves with full support. Explicit counterexamples are constructed on projective space using ideal sheaves of arithmetically Cohen–Macaulay subschemes. Lin...

Canonical Continuous Double–Turán Inequalities and a Derivative-Shift Barrier for the Riemann Xi Kernel

This preprint develops a continuous-parameter form of the double–Turán inequalities for a broad class of even admissible kernels. After introducing a canonical entire continuation of normalized Mellin coefficients, it proves strict positivity of the associated continuous double–T...

An Explicit Cox-Graded Complex with Chamber-Dependent Homology on Six Quotient Stacks

This preprint constructs an explicit four-term Cox-graded complex over an eight-variable Cox ring equipped with a rank-three torus grading and studies its restrictions to six quotient stacks arising from prescribed monomial semistable opens. The same complex has different homolog...

Smoothness of Concise Border-Rank-Five Forms on Veronese Secant Varieties

This preprint proves that every point of the fifth Veronese secant variety whose first catalecticant has rank five is smooth. Equivalently, every concise form in five essential variables with border rank five is a smooth point of the ambient fifth secant variety. Consequently, th...

Smoothness of Concise Border-Rank-Five Forms on Veronese Secant Varieties

This preprint proves that every point of the fifth Veronese secant variety whose first catalecticant has rank five is smooth. Equivalently, every concise form in five essential variables with border rank five is a smooth point of the ambient fifth secant variety. Consequently, th...

Counterexamples to Park's Coherent-Sheaf Conjecture and a Bounded-Edge MCM Extension

This paper disproves Park’s conjectural extension of asymptotic syzygy nonvanishing from line bundles to arbitrary coherent sheaves with full support. Explicit counterexamples are constructed on projective space using ideal sheaves of arithmetically Cohen–Macaulay subschemes. Lin...

Non-Split Ulrich Defects and a Two-Component Conductor Blowup in a Determinantal Degeneration

This paper studies a determinantal degeneration arising from a rank-one matrix cone and analyzes the interaction among a non-split defect module, Ulrich-type structures, conductor geometry, and birational modifications. The defect is described by a globally non-split extension, a...

Non-Split Ulrich Defects and a Two-Component Conductor Blowup in a Determinantal Degeneration

This paper studies a determinantal degeneration arising from a rank-one matrix cone and analyzes the interaction among a non-split defect module, Ulrich-type structures, conductor geometry, and birational modifications. The defect is described by a globally non-split extension, a...

Harmonic Theta-Mode Dominance and Superlinear Real-Zero Growth for the Riemann–Jacobi Kernel

This preprint studies the distinct real zeros of high derivatives of the Riemann–Jacobi kernel. It proves that their number grows faster than every fixed linear multiple of the differentiation order. The proof represents individual theta modes through generalized Bell polynomials...

Geometric-Series Valuations and Frobenius Initial Forms for the Krattenthaler–Müller Sequence

This paper resolves Conjecture 43 of Krattenthaler and Müller concerning the p-adic divisibility of the auxiliary integer sequence arising in Romik’s hypergeometric description of the Taylor coefficients of the Jacobi theta constant. A uniform valuation theorem is proved for ever...

Positive-Definite Boundary Correlations and Fourier Zero Strips: Resolution of Csordas' Open Problem 4.12

This paper gives a necessary and sufficient positive-definiteness criterion for confining the zeros of Fourier transforms of real even kernels with super-Gaussian decay to a prescribed horizontal strip. The criterion is formulated in terms of explicit boundary correlation kernels...

Profinite Vanishing of Fixed Columns in Romik's Matrix: Conjecture 47(2) and the Pure-Periodicity Clause in Conjecture 47(1)

This paper studies the fixed-column sequences in Romik’s matrix that appear in Conjecture 47 of Krattenthaler and Müller. It proves Conjecture 47(2) and establishes a stronger conclusion: every fixed-column sequence is eventually zero modulo every prescribed integer. Equivalently...

Positive-Definite Boundary Correlations and Fourier Zero Strips: Resolution of Csordas' Open Problem 4.12

This paper gives a necessary and sufficient positive-definiteness criterion for confining the zeros of Fourier transforms of real even kernels with super-Gaussian decay to a prescribed horizontal strip. The criterion is formulated in terms of explicit boundary correlation kernels...