Abstract
In [1] E. Bombieri showed that ¦4K¦ always yields a holomorphic map for surfaces of fundamental type and that ¦3K¦ does not yield a holomorphic map for such surfaces with pg=2 and c 21 ¦X¦=1. In this note we prove the existence of such surfaces and give a complete description of them. We prove that Torelli's local theorem is true, i.e., that the mapping of periods from the space of moduli into the space of periods is étale; we calculate the number of moduli and we show that the space of moduli is nonsingular.
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Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 623–632, October, 1974.
The author expresses his thanks to his scientific director I. R. Shafarevich for his constant interest in my work; he also thanks Ki for useful discussions.
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Todorov, A.N. Surfaces of fundamental type with geometric genus 2 and c 21 ¦X¦=1. Mathematical Notes of the Academy of Sciences of the USSR 16, 964–968 (1974). https://doi.org/10.1007/BF01104265
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DOI: https://doi.org/10.1007/BF01104265