$\mathbb{Z}_2^2$-actions on Horikawa surfaces

DOI10.1007/S00229-021-01303-9arXiv2102.12270MaRDI QIDQ6361445

Publication date: 24 February 2021

Abstract: Minimal algebraic surfaces of general type

X

such that

K_{X}^{2} = 2 c h i (m a t h c a l O_{X}) - 6

or

K_{X}^{2} = 2 c h i (m a t h c a l O_{X}) - 5

are called Horikawa surfaces. In this note we study

m a t h b b Z_{2}^{2}

-actions on Horikawa surfaces. The main result is that all the connected components of Gieseker's moduli space of canonical models of surfaces of general type with invariants satisfying these relations contain surfaces with

m a t h b b Z_{2}^{2}

-actions.

Mathematics Subject Classification ID

Surfaces of general type (14J29)

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