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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Biregular models of log Del Pezzo surfaces with rigid singularities
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by Muhammad Imran Qureshi HTML | PDF
Math. Comp. 88 (2019), 2497-2521 Request permission

Abstract:

We construct biregular models of families of log Del Pezzo surfaces with rigid cyclic quotient singularities such that a general member in each family is wellformed and quasismooth. Each biregular model consists of infinite series of such families of surfaces; parameterized by the natural numbers $\mathbb {N}$. Each family in these biregular models is represented by either a codimension 3 Pfaffian format modelled on the Plücker embedding of $\mathrm {Gr}(2,5)$ or a codimension 4 format modelled on the Segre embedding of $\mathbb {P}^2 \times \mathbb {P}^2$. In particular, we show the existence of two biregular models in codimension 4 which are biparameterized, giving rise to an infinite series of models of families of log Del Pezzo surfaces. We identify those biregular models of surfaces which do not admit a $\mathbb {Q}$-Gorenstein deformation to a toric variety.
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Additional Information
  • Muhammad Imran Qureshi
  • Affiliation: Department of Mathematics, SBASSE Lahore University of Management Sciences (LUMS), Lahore, Pakistan; and Mathematisches Institut, Universität Tübingen, Germany
  • MR Author ID: 948483
  • Email: i.qureshi@maths.oxon.org
  • Received by editor(s): November 28, 2017
  • Received by editor(s) in revised form: September 16, 2018
  • Published electronically: April 3, 2019
  • Additional Notes: This research was supported by a Higher Education Commission (HEC)’s NRPU grant 5906/Punjab/NRPU/RD/HEC/2016 and a fellowship of the Alexander von Humboldt Foundation.
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2497-2521
  • MSC (2010): Primary 14J10, 14M07, 14J45, 14Q10
  • DOI: https://doi.org/10.1090/mcom/3432
  • MathSciNet review: 3957903