Seshadri constants on blow‐ups of Hirzebruch surfaces

Krishna Hanumanthu, Cyril J. Jacob, B. N. Suhas and Amit Kumar Singh

Mathematische Nachrichten, 2025, vol. 298, issue 2, 437-455

Abstract: Let e,r≥0$e,r \ge 0$ be integers and let Fe:=P(OP1⊕OP1(−e))$\mathbb {F}_e: = \mathbb {P}(\mathcal {O}_{\mathbb {P}^1} \oplus \mathcal {O}_{\mathbb {P}^1}(-e))$ denote the Hirzebruch surface with invariant e$e$. We compute the Seshadri constants of an ample line bundle at an arbitrary point of the r$r$‐point blow‐up of Fe$\mathbb {F}_e$ when r≤e−1$r \le e-1$ and at a very general point when r=e$r=e$ or r=e+1$r=e+1$. We also discuss several conjectures on linear systems of curves on the blow‐up of Fe$\mathbb {F}_e$ at r$r$ very general points.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202400018

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:298:y:2025:i:2:p:437-455

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 ().