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Claudia Stadlmayr - Which rational double points occur on del Pezzo surfaces?

epiga:7041 - Épijournal de Géométrie Algébrique, November 29, 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.7041
Which rational double points occur on del Pezzo surfaces?

We determine all configurations of rational double points that occur on RDP del Pezzo surfaces of arbitrary degree and Picard rank over an algebraically closed field $k$ of arbitrary characteristic ${\rm char}(k)=p \geq 0$, generalizing classical work of Du Val to positive characteristic. Moreover, we give simplified equations for all RDP del Pezzo surfaces of degree $1$ containing non-taut rational double points.

Volume: Volume 5
Published on: November 29, 2021
Accepted on: November 29, 2021
Submitted on: January 4, 2021
Keywords: Mathematics - Algebraic Geometry,14J17, 14J26, 14B05, 14G17