Projective hypersurfaces with many singularities of prescribed types

Eugenii Shustin*, Eric Westenberger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Patchworking of singular hypersurfaces is used to construct projective hypersurfaces with prescribed singularities. For all n ≥ 2, an asymptotically proper existence result is deduced for hypersurfaces in Pn with singularities of corank at most 2 prescribed up to analytical or topological equivalence. In the case of T-smooth hypersurfaces with only simple singularities, the result is even asymptotically optimal, that is, the leading coefficient in the sufficient existence condition cannot be improved, which is new even in the case of plane curves. Furthermore, an asymptotically proper existence result is proved for hypersurfaces in Pn with quasihomogeneous singularities. The estimates substantially improve all known (general) existence results for hypersurfaces with these singularities.

Original languageEnglish
Pages (from-to)609-624
Number of pages16
JournalJournal of the London Mathematical Society
Volume70
Issue number3
DOIs
StatePublished - Dec 2004

Funding

FundersFunder number
Alexander von Humboldt-StiftungGR-640/9-1 DFG-Schwerpunkt
German-Israeli Foundation for Scientific Research and Development
Tel Aviv UniversityG-616-15.6/99

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