Riv. Mat. Univ. Parma, Vol. 11, No. 1, 2020

Francesca Acquistapace [a] and Fabrizio Broglia [a]

From complex to real analytic geometry

Pages: 1-8
Received: 10 January 2019
Accepted in revised form: 30 January 2019
Mathematics Subject Classification (2010): 14P15, 58A07, 32C25.
Keywords: Real analytic space, Global Nullstellensatz, \(17^{th}\) Hilbert problem.
Authors address:
[a]: University of Pisa, Dipartimento di Matematica, Largo Pontecorvo 5, Pisa, 56127, Italy

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Abstract: In this survey paper we look at the emergence of a good notion of real analytic space. Then we consider the global Nullstellensätze that have been proved both in the complex and in the real case. Finally we look at relations between a real global Nullstellensatz and Hilbert's \(17^{th}\) problem for global analytic functions and we give some conclusions.

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