arXiv subjects

Ryota Kotani

Publications and source records attributed to Ryota Kotani.

3 recordsLinked to original sources

arXiv2026

Principal twistor models and asymptotic hyperkähler metrics

Let $X$ be a conical symplectic variety admitting a crepant resolution $Y$. Based on the theory of universal Poisson deformations, we construct a complex manifold called the principal twistor model associated with $Y$. We prove a universality theorem for this model: if the regular locus of $X$ admits a hyperkähler cone metric, then the twistor space of any algebraic hyperkähler metric on $Y$ asymptotic to this cone metric is uniquely recovered by slicing the principal twistor model. As an application, we use this universality to study the moduli space of algebraic hyperkähler structures with asymptotic behavior, and show that it admits an inclusion into a finite-dimensional real vector space.

math.AG↗

arXiv2026

A Torelli-type theorem for hyperkähler quotients

In this paper, we investigate the moduli space of algebraic asymptotic hyperkähler structures on hyperkähler quotients arising from a quaternionic vector space $\mathbb{H}^n$. We consider the period map on this moduli space, and prove a Torelli-type theorem (i.e., the bijectivity of the period map) assuming the surjectivity of the Kirwan map. This work provides an algebro-geometric generalization of the Torelli-type theorem for ALE gravitational instantons by Kronheimer (1989). In particular, this theorem applies to toric hyperkähler varieties and Nakajima quiver varieties.

math.AG↗

arXiv2021

Bridging Pico-to-Nanonewtons with a Ratiometric Force Probe for Monitoring Nanoscale Polymer Physics Before Damage

Understanding the transmission of nanoscale forces in the pico-to-nanonewton range is important in polymer physics. While physical approaches have limitations in analyzing the local force distribution in condensed environments, chemical analysis using force probes is promising. However, there are stringent requirements for probing the local forces generated before structural damage. The magnitude of those forces corresponds to the range below covalent bond scission (from 200 pN to several nN) and above thermal fluctuation (several pN). Here, we report a conformationally flexible dual-fluorescence force probe with a theoretically estimated threshold of approximately 100 pN. This probe enables ratiometric analysis of the distribution of local forces in a stretched polymer chain network. Without changing the intrinsic properties of the polymer, the force distribution was reversibly monitored in real time. Chemical control of the probe location demonstrated that the local stress concentration is twice as biased at crosslinkers than at main chains, particularly in a strain-hardening region. Due to the high sensitivity, the percentage of stressed force probes was estimated to be more than 1000 times higher than the activation rate of a conventional mechanophore.

cond-mat.soft↗