Alladi Ramakrishnan Hall

Rationality of some moduli of chains of vector bundles

Saurav Chaudhury

IMSc, Chennai

Let $X$ be a compact Riemann surface of genus $\geq 2$. A chain on $X$ is a tuple
$(E_0,\dots,E_n; \phi_1, \dots, \phi_n)$ where $E_i$ are vector bundles on $X$ and $\phi_i: E_i
\to E_{i-1}$ are morphisms between vector bundles. One has a concept of stability dependent on
real parameters $\theta \in \mathbb{R}^{n+1}$ for these chains which leads to the construction of
the moduli space of $\theta$-stable holomorphic chains of type $\underline{t}$ denoted
$M_\theta^s(\underline{t})$. These moduli spaces allow for a moduli theoretic interpretation of
the fixed point locus of $\mathbb{G}_m$ action on the moduli of Higgs bundles.
We study the birational geometry of the moduli of chains of type $\underline{t}$ on $X$, which
are stable with respect to a fixed parameter $\theta$. For suitable $\underline{t}$ and $\theta$,
we establish the rationality of these moduli spaces. This is joint work with S. Manikandan.