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Iskovskikh Seminar
September 30, 2020 15:00, Moscow, online

Surface fibrations with large equivariant automorphism groups

Yi Gu

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Abstract: Given a fibration $f: X\to C$ from a smooth projective surface $X$ to a smooth curve $C$ over an arbitrary algebraically closed field $k$. The equivariant automorphism group is
$$\mathbb{E}(X/C):=\{ (\tau,\sigma) | \tau\in \mathrm{Aut}_k(X), \sigma\in \mathrm{Aut}_k(C), f\circ \tau =\sigma\circ f \}$$
with natural composition law.
$$\xymatrix{ X\ar[rr]_\sim^\tau \ar[d]_f&& X \ar[d]^fC \ar[rr]_\sim^\sigma && C }$$
This group is an important invariant of the fibration $f$ and sometimes that of the surface $X$. In this talk, we will give a classification of those relatively minimal surface fibrations whose equivariant automorphism group $\mathbb{E}(X/C)$ is infinite. As an application, we will also discuss the Jordan property of the automorphism group of a minimal surface of Kodaira dimension one.

Language: English

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