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Explicit Schoen surfaces
TL;DR: In this paper, the authors give an explicit construction for the Schoen surfaces by computing equations for their canonical images, which are $40$-nodal complete intersections of a quadric and the Igusa quartic in $\mathbb P^4$.
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Abstract: We give an explicit construction for the $4$-dimensional family of Schoen surfaces by computing equations for their canonical images, which are $40$-nodal complete intersections of a quadric and the Igusa quartic in $\mathbb P^4$. We then study a particularly interesting example, with $240$ automorphisms and maximal Picard number.
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Citations
Biregular and birational geometry of quartic double solids with 15 nodes
TL;DR: In this article, it was shown that if a del Pezzo variety of degree 2 has exactly 15 nodes then the corresponding quadric is a hyperplane section of the Igusa quartic or equivalently, all such delPezzo varieties are members of one particular linear system on the Coble fourfold.
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Explicit Nikulin configurations on Kummer surfaces
Xavier Roulleau,Alessandra Sarti +1 more
TL;DR: In this paper, the authors generalise the construction to Kummer surfaces with a weaker restriction on the degree of the polarization and describe some cases where the previous construction does not work.
3
Inverse designing surface curvatures by deep learning
TL;DR: This work explores surface curvature as a design modality and presents a deep learning framework to produce topologies with as-desired curvature profiles and demonstrates successful generalization beyond both the design and data space by inverse designing topologies that mimic the curvature profile of trabecular bone, spinodoid topologies, and periodic nodal surfaces.
A pair of rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not the bidisk
TL;DR: In this paper, the authors constructed two complex-conjugated rigid surfaces with universal cover invariants (p_g=q=2$ and K^2=8$ ) and showed that these are the unique surfaces with these invariants and the Albanese map of degree 2.
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Addendum : « Inégalités numériques pour les surfaces de type général »
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation ( http://www.numdam.org/legal.html).