The universal cover of the second-type locus of a cubic

Frank Gounelas

Abstract

We prove that the surface of second-type lines on a general cubic fourfold has fundamental group of order two. Its universal cover, constructed by Huybrechts, is obtained by considering the two ramification points of the Gauss map along each second-type line.

Disclosure

“mental group of the second- type locus in the first place. I am also indebted to Alexis Kouvidakis for explaining to me most things I know about cubics. This work was supported by the ERC Synergy Grant HyperK (ID 854361). The OpenAI LLM GPT-4.6-Sol was used in the writing and editing of this paper. 2. The second-type surface and its double cover Write X = {g = 0} ⊂ P(V ), dim V = 6, 3 ∨ where g ∈ Sym (V ) is a cubic e”

PDF page 2
Classification
Drafting limited passages
Multiplier
5
Verified

Structural counts

Pages 11 pdf
Theorems 1 source
Lemmas 5 source
Propositions 1 source
Corollaries 1 source
Definitions 0 source
Displayed equations 91 source
Bibliography entries 10 source
Appendix pages 0 estimated

Count notes

  • Source counts use the expanded primary TeX file arxiv1.tex.
  • Appendix pages include the first PDF page with an explicit Appendix heading through the final page.