The exponential sequence in real algebraic geometry and Harnack’s inequality for proper reduced real schemes. (English) Zbl 1055.14058
Summary: We introduce the analytification \(X^{an}\) of a scheme \(X\) locally of finite type over \(\mathbb{R}\). On \(X^{an}\) one has an exponential sequence if \(X\) is reduced. This exponential sequence gives rise to an analytic description of the Picard group \(\text{Pic}(X)\) if \(X\) is proper and reduced. Using this description we generalize Harnack’s inequality [A. Harnack, Math. Ann. 10, 189–198 (1876; JFM 08.0438.01)] for real algebraic curves to arbitrary proper reduced real schemes.
Keywords:
analytificationCitations:
JFM 08.0438.01References:
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