A note on special cubic fourfolds of small discriminants-Reference-Cited by-同舟云学术

A note on special cubic fourfolds of small discriminants

Published:2021-08-26 Issue:5 Volume:33 Page:1137-1155
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Truong Hoang Le¹,Yen Hoang Ngoc²

Affiliation:

1. Mathematik und Informatik , Universität des Saarlandes , Campus E2 4, 66123 Saarbrücken , Germany ; and Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam; and Thang Long Institute of Mathematics and Applied Sciences, Hanoi, Vietnam

2. The Department of Mathematics , Thai Nguyen University of Education , 20 Luong Ngoc Quyen Street , Thai Nguyen City , Thai Nguyen Province , Vietnam

Abstract

Abstract In this paper, our purpose is to give a characterization of the generic special cubic fourfold which contains a smooth rational surface of degree 9 not homologous to a complete intersection. As corollaries, we will give an explicit construction of families of smooth surfaces in generic special cubic fourfolds X ∈ 𝒞 δ

{X\in\mathcal{C}_{\delta}}

for 6 < δ ≤ 30

{6<\delta\leq 30}

and δ ≡ 0 ( mod 6 )

{\delta\equiv 0~{}(\bmod~{}6)}

. This applies in particular to give an explicit construction of two different liaison class of smooth surfaces in all such special cubic fourfolds with the prescribed invariants.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2020-0355/pdf

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