Singular rational curves on elliptic K3 surfaces

Jonas Baltes

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2701-2714

Abstract: We show that on every elliptic K3 surface there are rational curves (Ri)i∈N$(R_i)_{i\in \mathbb {N}}$ such that Ri2→∞$R_i^2 \rightarrow \infty$, that is, of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to P(ΩX)$\mathbb {P}(\Omega _X)$ is dense in the Zariski topology. As an application, we give a simple proof of a theorem of Kobayashi in the elliptic case, that is, there are no globally defined symmetric differential forms.

Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200228

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:7:p:2701-2714

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().