Terry Dekun Song

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20242026

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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.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

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