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Mathematics Seminar Date: Wednesday, 28 August 2024 Time: 3:30 PM Venue: Seminar Hall A criteria for rationality of moduli of chains Saurav Holme Choudhury Institute of Mathematical Sciences, Chennai. 28-08-24 Abstract 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.
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