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A note on special cubic fourfolds of small discriminants

Hoang Le Truong and Hoang Ngoc Yen
From the journal Forum Mathematicum

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 X𝒞δ for 6<δ30 and δ0(mod6). 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.


Communicated by Shigeharu Takayama


Funding source: National Foundation for Science and Technology Development

Award Identifier / Grant number: 101.04-2019.309

Funding source: Vietnam Academy of Science and Technology

Award Identifier / Grant number: ICRTM02-2020.05

Funding statement: The first author was partially supported by the Alexander von Humboldt Foundation and the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2019.309. The second author was partially supported by Grant number ICRTM02-2020.05, awarded in the internal grant competition of International Center for Research and Postgraduate Training in Mathematics, Hanoi.

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Received: 2020-12-22
Revised: 2021-07-30
Published Online: 2021-08-26
Published in Print: 2021-09-01

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