Connectivity of hyperplane sections of domains. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Varbaro, Matteo
• Is Part Of: Communications in algebra. Volume 47:Issue 6(2019)
• Page Start: 2540
• Page End: 2547
• Publication Date: 2019-06-03
• Subjects: Connectedness -- domain -- hyperplane sections -- Lyubeznik complex -- nerve complex; 13G05 -- 14F45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1492593
• Languages: English
• ISSNs: 0092-7872

Abstract

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.