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Kenta Watanabe

Publications and source records attributed to Kenta Watanabe.

15 recordsLinked to original sources
arXiv2026

360CityArena: A Realistic Virtual Urban Navigation Benchmark for Embodied Agents

We present 360CityArena, a benchmark for evaluating the urban exploration capabilities of embodied agents within a photorealistic environment constructed from 360-degree videos. Existing outdoor benchmarks either lack sufficient photorealism or complexity, resulting in a considerable gap from real-world urban environments. 360CityArena is built on a realistic reconstruction of the Akihabara district in Tokyo, Japan, using 602 360-degree video segments covering 85 streets, and consists of 175 meticulously human-crafted tasks. It encompasses three task categories: Environment Understanding, Path Reasoning, and Spatial Reasoning, covering fundamental abilities required for urban exploration, such as localization, landmark search, path planning, and relational spatial reasoning, thereby enabling comprehensive evaluation in realistic urban scenes. Our evaluation using state-of-the-art LMM-based agents shows that even the strongest model, Gemini 2.5 Flash, performs far below human level (human: 77.3% vs. Gemini 2.5 Flash: 17.1%), revealing substantial challenges that remain in city-scale embodied navigation and reasoning. 360CityArena provides a necessary and challenging testbed for photorealistic urban-district navigation and spatial reasoning.

cs.CV↗
arXiv2026

Second gonality of smooth aCM curves on quartic surfaces in $\mathbb{P}^3$

For a smooth irreducible curve $C$, its second gonality $d_2$ is defined to be the minimum integer $d$ such that $C$ admits a linear series $g_d^2$. In this paper, we compute the second gonality of a smooth aCM curve $C$ lying on a smooth quartic surface in $\mathbb{P}^3$, whose Clifford index is computed by a net on $C$.

math.AG↗
arXiv2026

Paper Reconstruction Evaluation: Evaluating Presentation and Hallucination in AI-written Papers

This paper introduces the first systematic evaluation framework for quantifying the quality and risks of papers written by modern coding agents. While AI-driven paper writing has become a growing concern, rigorous evaluation of the quality and potential risks of AI-written papers remains limited, and a unified understanding of their reliability is still lacking. We introduce Paper Reconstruction Evaluation (PaperRecon), an evaluation framework in which an overview (overview.md) is created from an existing paper, after which an agent generates a full paper based on the overview and minimal additional resources, and the result is subsequently compared against the original paper. PaperRecon disentangles the evaluation of the AI-written papers into two orthogonal dimensions, Presentation and Hallucination, where Presentation is evaluated using a rubric and Hallucination is assessed via agentic evaluation grounded in the original paper source. For evaluation, we introduce PaperWrite-Bench, a benchmark of 51 papers from top-tier venues across diverse domains published after 2025. Our experiments reveal a clear trade-off: while both ClaudeCode and Codex improve with model advances, ClaudeCode achieves higher presentation quality at the cost of more than 10 hallucinations per paper on average, whereas Codex produces fewer hallucinations but lower presentation quality. This work takes a first step toward establishing evaluation frameworks for AI-driven paper writing and improving the understanding of its risks within the research community.

cs.CL↗
arXiv2024

A remark on the conjecture of Donagi-Morrison

Let $X$ be a K3 surface, let $C$ be a smooth curve of genus $g$ on $X$, and let $A$ be a base point free and primitive line bundle $g_d^r$ on $C$ with $d\geq4$ and $r\geq\sqrt{\frac{d}{2}}$. In this paper, we prove that if $g>2d-3+(r-1)^2$, then there exists a line bundle $N$ on $X$ which is adapted to $|C|$ such that $|A|$ is contained in the linear system $|N\otimes\mathcal{O}_C|$, and ${\rm{Cliff}}(N\otimes\mathcal{O}_C)\leq {\rm{Cliff}}(A)$.

math.AG↗
arXiv2023

Lifts of line bundles on curves on K3 surfaces

Let $X$ be a K3 surface, let $C$ be a smooth curve of genus $g$ on $X$, and let $A$ be a line bundle of degree $d$ on $C$. Then a line bundle $M$ on $X$ with $M\otimes\mathcal{O}_C=A$ is called a lift of $A$ . In this paper, we prove that if the dimension of the linear system $|A|$ is $r\geq2$, $g>2d-4+r(r-1)$, $d\geq 2r+4$, and $A$ computes the Clifford index of $C$, then there exists a base point free lift $M$ of $A$ such that the general member of $|M|$ is a smooth curve of genus $r$. In particular, if $|A|$ is a base point free net which defines a double covering $π:C\longrightarrow C_0$ of a smooth curve $C_0\subset\mathbb{P}^2$ of degree $k\geq 4$ branched at distinct $6k$ points on $C_0$, then, by using the aforementioned result, we can also show that there exists a 2:1 morphism $\tildeπ:X\longrightarrow \mathbb{P}^2$ such that $\tildeπ|_C=π$.

math.AG↗
arXiv2022

On the classification of non-aCM curves on quintic hypersurfaces in $\mathbb{P}^3$

In this paper, we call a sub-scheme of dimension one in $\mathbb{P}^3$ a curve. It is well known that the arithmetic genus and the degree of an aCM curve $D$ in $\mathbb{P}^3$ is computed by the $h$-vector of $D$. However, for a given curve $D$ in $\mathbb{P}^3$, the two invariants of $D$ do not tell us whether $D$ is aCM or not. In this paper, we give a classification of curves on a smooth quintic hypersurface in $\mathbb{P}^3$ which are not aCM.

math.AG↗
arXiv2021

New examples of Weierstrass semigroups associated with a double covering of a curve on a Hirzebruch surface of degree one

Let $φ:Σ_1\longrightarrow \mathbb{P}^2$ be a blow up at a point on $\mathbb{P}^2$. Let $C$ be the proper transform of a smooth plane curve of degree $d\geq 4$ by $φ$, and let $P$ be a point on $C$. Let $π:\tilde{C}\longrightarrow C$ be a double covering branched along the reduced divisor on $C$ obtained as the intersection of $C$ and a reduced divisor in $|-2K_{Σ_1}|$ containing $P$. In this paper, we investigate the Weierstrass semigroup $H(\tilde{P})$ at the ramification point $\tilde{P}$ of $π$ over $P$, in the case where the intersection multiplicity at $φ(P)$ of $φ(C)$ and the tangent line at $φ(P)$ of $φ(C)$ is $d-1$.

math.AG↗
arXiv2020

ACM bundles of rank 2 on quartic hypersurfaces in $\mathbb{P}^3$ and Lazarsfeld-Mukai bundles

Let $X$ be a smooth quartic hypersurface in $\mathbb{P}^3$. By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on $X$ is globally generated, then it is the Lazarsfeld-Mukai bundle $E_{C,Z}$ associated with a smooth curve $C$ on $X$ and a base point free pencil $Z$ on $C$. In this paper, we will focus on the classification of such bundles on $X$ to investigate aCM bundles of rank 2 on $X$. Concretely, we will give a necessary condition for a rank 2 vector bundle of type $E_{C,Z}$ to be indecomposable initialized and aCM, in the case where the class of $C$ in Pic($X$) is contained in the sublattice of rank 2 generated by the hyperplane class of $X$ and a non-trivial initialized aCM line bundle on $X$.

math.AG↗
arXiv2018

ACM line bundles on polarized K3 surfaces

An ACM bundle on a polarized algebraic variety is defined as a vector bundle whose intermediate cohomology vanishes. We are interested in ACM bundles of rank one with respect to a very ample line bundle on a K3 surface. In this paper, we give a necessary and sufficient condition for a non-trivial line bundle $\mathcal{O}_X(D)$ on $X$ with $|D|=\emptyset$ and $D^2\geq L^2-6$ to be an ACM and initialized line bundle with respect to $L$, for a given K3 surface $X$ and a very ample line bundle $L$ on $X$.

math.AG↗
arXiv2017

Electrical control of a solid-state flying qubit

Solid-state approaches to quantum information technology are attractive because they are scalable. The coherent transport of quantum information over large distances, as required for a practical quantum computer, has been demonstrated by coupling solid-state qubits to photons1. As an alternative approach for a spin-based quantum computer, single electrons have also been transferred between distant quantum dots in times faster than their coherence time2, 3. However, there have been no demonstrations to date of techniques that can coherently transfer scalable qubits and perform quantum operations on them at the same time. The resulting so-called flying qubits are attractive because they allow for control over qubit separation and non-local entanglement with static gate voltages, which is a significant advantage over other solid-state qubits in confined systems for integration of quantum circuits. Here we report the transport and manipulation of qubits over distances of 6 microns within 40 ps, in an Aharonov-Bohm ring connected to two-channel wires that have a tunable tunnel coupling between channels. The flying qubit state is defined by the presence of a travelling electron in either channel of the wire, and can be controlled without a magnetic field. Our device has shorter quantum gates, longer coherence lengths (~86 μm at 70 mK), and shorter operation times (~10 ps or 100 GHz) than other solid-state flying qubit implementations4, 5, which makes our solid-state flying qubit potentially scalable.

cond-mat.mes-hall↗
arXiv2017

Unstable Lazarsfeld-Mukai bundles of rank 2 on a certain K3 surface of Picard number 2

Let $g$ and $c$ be any integers satisfying $g\geq3$ and $0\leq c\leq \lfloor\frac{g-1}{2}\rfloor$. It is known that there exists a polarized K3 surface $(X,H)$ such that $X$ is a K3 surface of Picard number 2, and $H$ is a very ample line bundle on $X$ of sectional genus $g$ and Clifford index $c$, by Johnsen and Knutsen([J-K] and [Kn]). In this paper, we give a necessary and sufficient condition for a Lazarsfeld-Mukai bundles of rank 2 associated with a smooth curve $C$ belonging to the linear system $|H|$ and a base point free pencil on $C$ not to be $H$-slope stable.

math.AG↗
arXiv2017

On the splitting of Lazarsfeld-Mukai bundles on K3 surfaces II

In this paper, we say that a rank 2 bundle splits if it is given by an extension of two line bundles. In the previous works, we gave a necessary condition for Lazarsfeld-Mukai bundles of rank 2 to split, under a numerical condition ([W2], Theorem 3.1). We gave the splitting types of them on a smooth quartic hypersurface in P3 ([W2], Proposition 3.1) as a corollary of it. However, the assertion of it contains a few mistakes. In this paper, we correct them, and give an application of the results in [W2].

math.AG↗
arXiv2015

Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles

Previously, many people have studied a stability of vector bundles of given rank and Chern classes on algebraic varieties. Recently, we are interested in the slope stability of the rank 2 Lazarsfeld-Mukai bundle $E_{C,Z}$ on a K3 surface $X$ associated to a very ample smooth curve $C$ on $X$ and a base point free pencil $Z$ on $C$ with respect to $\mathcal{O}_X(C)$. In this paper, we will give a sufficient condition for such a Lazarsfeld-Mukai bundle $E_{C,Z}$ to be $\mathcal{O}_X(C)$-slope semistable by ACM line bundles with respect to $\mathcal{O}_X(C)$.

math.AG↗