arXiv subjects

Chiwon Yoon

Publications and source records attributed to Chiwon Yoon.

3 recordsLinked to original sources

arXiv2026

Nef Cones of the Hilbert Schemes of Points on Generalized Cayley K3 Surfaces

We study the nef cones of Hilbert schemes of points on generalized Cayley K3 surfaces $S_a$. For the Hilbert squares $S_a^{[2]}$ with $a=1,2$, we determine the nef and effective cones by combining Beauville involutions with the Bayer--Macrì wall description and explicit lattice calculations. In the Cayley case $a=1$, we further construct an explicit rational polyhedral fundamental domain for the action of the automorphism group on the nef effective cone. For arbitrary $a$ and $n\ge\lfloor a^2/4\rfloor+3$, we determine the nef and Mori cones using explicit divisor classes whose nefness follows from the Mukai lattice description, together with curve classes obtained from pencils on smooth curves.

math.AG↗

arXiv2026

Nef cone decompositions for nested Hilbert schemes of points on surfaces

Let $S$ be a smooth projective surface with $q(S)=0$. We give numerical criteria for the nef cones of $S^{[n,n+1]}$ and $S^{[1,n]}$ to decompose as sums of pullbacks of nef cones under their natural morphisms. These criteria recover the known decompositions for the projective plane, Hirzebruch surfaces, and Picard rank one K3 surfaces, and apply to del Pezzo surfaces with $2\le K_S^2\le7$. For a del Pezzo surface of degree one, we show that the corresponding pullback decompositions fail for both $S^{[n,n+1]}$ and $S^{[1,n]}$.

math.AG↗

arXiv2026

Secant variety and syzygies of Hilbert scheme of two points

In this paper, we prove that $\mathrm{Sec} (X^{[2]})$ features the identifiability under the Grothendieck-Plücker embedding $X^{[2]} \hookrightarrow \PP^N$ when $X$ is embedded by a $4$-very ample line bundle. We also prove that the embedding $X^{[2]} \hookrightarrow \PP^N$ satisfies Green's condition $(N_p)$ when the embedding of $X$ is positive enough. Accordingly, the singular locus of $\mathrm{Sec} (X^{[2]})$ is exactly $X^{[2]}$ when the embedding of $X$ is positive enough. As an application, we describe the geometry of a resolution of singularities from the secant bundle to $\mathrm{Sec}(X^{[2]})$ when $X$ is a surface.

math.AG↗