Asian Journal of Mathematics

Volume 15 (2011)

Number 3

Forty questions on singularities of algebraic varieties

Pages: 417 – 436



Herwig Hauser

Josef Schicho


The reader will find in this article a collection of problems, questions and exercises related to the singularities of algebraic and analytic varieties. Many of them are inspired by the work and mathematical conception of Hironaka: they are concrete, involve basic ideas and techniques from geometry and algebra, and they can immediately be attacked from scratch. Some problems rely on or use results proven by Hironaka. Simple and double asterisques indicate the more difficult problems; they may potentially serve as a topic of future research.


Algebraic geometry; analytic geometry; singularities; resolution

2010 Mathematics Subject Classification

14B05, 14B12, 32S05, 32S45

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