Searcharxiv⌕ Search

arXiv subjects

In-Kyun Kim

Publications and source records attributed to In-Kyun Kim.

At least 19 recordsLinked to original sources
arXiv2026

Spectral pairs of Newton non-degenerate polynomials with isolated singularities

We give a formula for the spectral pairs of Newton non-degenerate polynomials with isolated singularities. This is a revised version of a conjecture proposed by Steenbrink fifty years ago. Although this conjecture fails in the non-simplicial Newton polytope case, we can find the correction term using the intersection complexes and the primitive intersection cohomologies of toric varieties associated with non-simplicial compact faces. To verify the correctness of the formula, we provide a sample code for Singular which computes the spectral pairs and compares the output with that of sppairs in Singular for the three variable case.

math.AG↗
arXiv2026

Issue-Specific Polarization and Cohesion in a Multi-Party Legislature: Integrating the Latent Space Item Response Model with Topic-Based Regression

We develop a two-stage, cut-posterior Bayesian framework for quantifying issue-specific legislative alignment in multi-party systems. The approach integrates a Latent Space Item Response Model (LSIRM), embedding legislators and bills in a shared Euclidean space, with Bayesian beta regression using text-derived topic proportions as bill-level covariates. The resulting legislator- and issue-specific coefficients allow polarization and cohesion to be compared across policy domains. The beta-regression layer must not feed back into the estimated latent geometry, so that the two components target a cut posterior. We estimate it with a two-stage Multiple-Imputation procedure that propagates uncertainty in the latent positions into every downstream quantity. In the 17th Korean National Assembly, fiscal domains such as Taxation and Grants and Local Government Budget show sharp polarization with tight within-party clustering, whereas Armed Services, Patriots, and Veterans exhibits weak party structuring and greater intra-party variability. The Democratic Labor Party forms a distinct cluster on several issues even where the two major parties are not strongly polarized, showing that legislative conflict escapes a single left--right ordering. The framework supports analysis of issue-structured voting in legislatures where one-dimensional ideal point models are unreliable.

stat.AP↗
arXiv2026

Polarized cylinders on blow-ups of weighted projective planes

We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m+4$ points in general position on the weighted projective plane $\mathbb{P}(1,1,m)$. These surfaces appear naturally as weighted hypersurfaces or quasi-smooth complete intersections.

math.AG↗
arXiv2026

Flexibility of affine cones over blow-ups of weighted projective planes

Let $S_m^n$ be the surface obtained by blowing up $\mathbb{P}(1,1,m)$ at $n$ general smooth points, where $m\geq2$. For every very ample Cartier divisor $H$ on $S_m^n$, we prove that $\mathrm{Affcone}_H(S_m^n)$ is flexible when $n\leq m+1$. For $n=m+2$ and $n=m+3$, we prove that $\mathrm{Affcone}_H(S_m^n)$ is generically flexible.

math.AG↗
arXiv2026

Cylinders in weighted Fano varieties

Cylinders in Fano varieties receives a lot of attentions recently from the viewpoints of birational geometry and unipotent geometry. In this article, we provide a survey of several known et new results concerning the anti-canonically polar cylindricity of quasi-smooth, well-formed weighted Fano complete intersections in weighted projective spaces.

math.AG↗
arXiv2026

Subtlety of oscillation indices of oscillatory integrals of real analytic functions

For a locally defined real analytic function $f$, we study the relation between the oscillation index of oscillatory integrals and the real log canonical threshold. The former is always negative, and its absolute value is greater than or equal to the latter. They coincide very often, but there are certain exceptional cases, and it is not very clear when the equality holds. In this note we give some sufficient conditions for the coincidence to hold or to fail. In the Newton-nondegenerate convenient homogeneous case, we show that the strict inequality holds if the number of variables $n$ is even and smaller than the degree $d$ of $f$ (or $f^{-1}(0)=\{0\}$), and the equality holds if $n$ is odd and $f^{-1}(0)=\{0\}$ (in particular, $d$ is even). The first assertion does not seem to be compatible with some standard formula in the literature, and there must be some error somewhere, although it does not seem easy to detect it inside this paper.

math.CV↗
arXiv2026

Some remarks on the generalized Hertling conjecture for Tjurina spectrum

We study the original version of the generalized Hertling conjecture on the variance of the Tjurina spectral numbers, which was proposed by Shi, Wang, and Zuo, and provide a sufficient condition for the original conjecture to fail, employing a theorem of Hertling in an essential way. We calculate certain examples using some codes in Singular.

math.AG↗
arXiv2026

Wall-crossing for K-moduli spaces of certain families of weighted projective hypersurfaces

We describe the K-moduli spaces of weighted hypersurfaces of degree $2(n+3)$ in $\mathbb{P}(1,2,n+2,n+3)$. We show that the K-polystable limits of these weighted hypersurfaces are also weighted hypersurfaces of the same degree in the same weighted projective space. This is achieved by an explicit study of the wall crossing for K-moduli spaces $M_w$ of certain log Fano pairs with coefficient $w$ whose double cover gives the weighted hypersurface. Moreover, we show that the wall crossing of $M_w$ coincides with variation of GIT except at the last K-moduli wall which gives a divisorial contraction. Our K-moduli spaces provide new birational models for some natural loci in the moduli space of marked hyperelliptic curves.

math.AG↗
arXiv2026

Tjurina spectrum and graded symmetry of missing spectral numbers

For a hypersurface isolated singularity defined by a convergent power series $f$, the Steenbrink spectrum can be defined as the Poincaré polynomial of the graded quotients of the $V$-filtration on the Jacobian ring of $f$. The Tjurina subspectrum is defined by replacing the Jacobian ring with its quotient by the image of the multiplication by $f$. We prove that their difference (consisting of missing spectral numbers) has a canonical graded symmetry. This follows from the self-duality of the Jacobian ring, which is compatible with the action of $f$ as well as the $V$-filtration. It implies for instance that the number of missing spectral numbers which are smaller than $(n{+}1)/2$ (with $n$ the number of variables) is bounded by $[(μ{-}τ)/2]$. We can moreover improve the estimate of Briançon-Skoda exponent in the semisimple monodromy case.

math.AG↗
arXiv2025

Automorphism groups and cylindricity of weighted hypersurface Fano threefolds

It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$ families, $15$ families have the property that general members are irrational, in particular, any of them has a finite automorphism group and is not cylindrical. In the present paper, we will observe the cylindricity and the full automorphism groups of every member in the remaining $20$ families. Moreover, we deal with the cylindricity of their forms.

math.AG↗
arXiv2023

K-polystability of the first secant varieties of rational normal curves

The first secant variety $Σ$ of a rational normal curve of degree $d \geq 3$ is known to be a $\mathbf{Q}$-Fano threefold. In this paper, we prove that $Σ$ is K-polystable, and hence, $Σ$ admits a weak Kähler-Einstein metric. We also show that there exists a $(-K_Σ)$-polar cylinder in $Σ$.

math.AG↗
arXiv2023

Spectrum of non-degenerate functions with simplicial Newton polytopes

We show a precise proof of Steenbrink's formula for the spectrum of convenient Newton non-degenerate functions, and prove the symmetry of combinatorial polynomials in the simplicial case. Combined with the modified Steenbrink conjecture for spectral pairs (that is, weighted spectrum) which is recently proved in that case, this simplifies quite a lot of their calculations in such a case. We also introduce the $Γ$-spectrum of simplicial convenient non-degenerate functions as a first approximation of the spectrum, generalizing Arnold's picture in the 2 variable case. Analyzing their difference, we can find simple formulas for weighted spectrum in the 3 or 4 variable case. This is proved by using the symmetry of combinatorial polynomials, and fails in the non-simplicial case. Combining these with the Yomdin-Steenbrink formula for the spectrum, we can prove a formula for the spectrum of certain non-isolated surface singularities with simplicial non-degenerate Newton boundaries. As a byproduct of these arguments, we find an example where the Yomdin-Steenbrink formula for spectral pairs does not hold because of fusions of compact faces under projections.

math.AG↗
arXiv2023

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$. Combining this with the result of Stibitz and Zhuang \cite{SZ19} on a relation between birational superrigidity and K-stability, we prove the K-stability of a birationally superrigid quasi-smooth Fano 3-fold weighted hypersurfaces of index $1$.

math.AG↗