Terry Dekun Song

activity

20242026

collaborators

8 papers

math.AG2026

Motivic quasimap wall-crossing for Grassmannians

Siddarth Kannan, Terry Dekun Song

We prove a wall-crossing formula for the Euler characteristics, considered as virtual mixed Hodge structures, of moduli spaces of $ε$ -stable quasimaps to the Grassmannian…

math.AG2026

Logarithmic Hilbert schemes of curves as weighted blow-ups and their integral Chow rings

Veronica Arena, Terry Dekun Song

The logarithmic Hilbert scheme of a logarithmic curve parametrizes subschemes on the expanded degenerations of the curve that are transverse to the boundary. We prove that the loga…

math.CO2026

Pólya enumeration, wreath product symmetric functions, and moduli spaces of curves

Siddarth Kannan, Terry Dekun Song

We develop a calculus for $S_{n}$ -equivariant Euler characteristics of moduli spaces of stable curves and stable maps. Our approach involves an enrichment of Pólya's cycle index poly…

math.AG2026

Topology of the Vakil--Zinger moduli space

Terry Dekun Song

We derive a set of generators for the rational homology of the desingularised genus one mapping space $M_{1, n} (P^{r}, d)$ constructed by Vakil--Zinger a…

math.AG2026

Virtual Hodge numbers of $M_{g, n} (P^{r}, d)$ : stability and calculations

Siddarth Kannan, Terry Dekun Song

We study $S_{n}$ -equivariant motivic invariants of the moduli space $M_{g, n} (P^{r}, d)$ of degree- $d$ maps from $n$ -pointed curves of genus $g$ to $\mathbb…

math.AG2025

Graph enumeration for moduli spaces of curves and maps

Siddarth Kannan, Terry Dekun Song

We develop a calculus based on graph enumeration for $S_{n}$ -equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford modul…

math.AG2024

The $S_{n}$ -equivariant Euler characteristic of $M_{1, n} (P^{r}, d)$

Siddarth Kannan, Terry Dekun Song

We compute the $S_{n}$ -equivariant topological Euler characteristic of the Kontsevich moduli space $M_{1, n} (P^{r}, d)$ . Letting $\overline{\mathcal{M}}_{…

math.AG2024

The dual complex of $M_{1, n} (P^{r}, d)$ via the geometry of the Vakil--Zinger moduli space

Siddarth Kannan, Terry Dekun Song

We study normal crossings compactifications of the moduli space of maps $M_{g, n} (P^{r}, d)$ , for $g = 0$ and $g = 1$ . In each case we explicitly determine the dua…

Motivic quasimap wall-crossing for Grassmannians

Logarithmic Hilbert schemes of curves as weighted blow-ups and their integral Chow rings

Pólya enumeration, wreath product symmetric functions, and moduli spaces of curves

Topology of the Vakil--Zinger moduli space

Virtual Hodge numbers of Mg,n​(Pr,d): stability and calculations

Graph enumeration for moduli spaces of curves and maps

The Sn​-equivariant Euler characteristic of M1,n​(Pr,d)

The dual complex of M1,n​(Pr,d) via the geometry of the Vakil--Zinger moduli space

Virtual Hodge numbers of $M_{g, n} (P^{r}, d)$ : stability and calculations

The $S_{n}$ -equivariant Euler characteristic of $M_{1, n} (P^{r}, d)$

The dual complex of $M_{1, n} (P^{r}, d)$ via the geometry of the Vakil--Zinger moduli space