Talk:Hirzebruch surface

Todo

• Describe the Hirzebruch surface in terms of a toric variety. This post https://wangweikun.com/math-ag-toric/toric-construction-of-hirzebruch-surface/ is super handy while going through this process
• Go through giving an explicit description using page 27 - 39 of https://arxiv.org/pdf/math/0507286.pdf (Manetti Deformation) since the charts come from the toric geometry/quotient geometry
• Relate the last construction to the construction with the symmetric algebra, this should demystify the presentation
• Also, given examples for the simple case of ${\mathcal {O}}(1)\oplus {\mathcal {O}}$
• Reference scrolls and how they are generalizations of this construction
• Describe relation to gonality of curves
• https://mathoverflow.net/questions/122952/on-a-hirzebruch-surface

Wundzer (talk) 02:06, 10 June 2020 (UTC)