Connectivity of hyperplane sections of domains. Issue 6 (3rd June 2019) - Varbaro, Matteo
Abstract: During the conference held in 2017 in Minneapolis for his 60th birthday, Gennady Lyubeznik proposed the following problem: Find a complete local domain R and an element x ∈ R having three minimal primes p 1, p 2 and p 3 such that p i + p j has height 2 for all i ≠ j and p 1 + p 2 + p 3 has height 4. In this note this beautiful problem will be discussed, and will be shown that the principle leading to the fact that such a ring cannot exist is false. The specific problem, though, remains open.