Symmetries and equations of smooth quartic surfaces with many lines

Veniani, Davide Cesare

doi:10.4171/rmi/1127

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…In fact in this case S is a determinantal quartic K3 surface, presented with three different models, hence Z is a hyperkähler fourfold. This construction is very classical, starting from [6], and the relations between the three models has been recently explored in [12,24,31].…”

Section: Consider Now Two Triplesmentioning

confidence: 99%

Hilbert squares of degeneracy loci

Fatighenti¹,

Meazzini²,

Mongardi³

et al. 2022

Preprint

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Let S be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in s . We prove that, under certain positivity conditions, its Hilbert square Hilb 2 (S) is isomorphic to the zero locus of a global section of an irreducible homogeneous vector bundle on a product of Grassmannians. Our construction involves a naturally associated Fano variety, and an explicit description of the isomorphism.

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Section: Consider Now Two Triplesmentioning

confidence: 99%

Hilbert squares of degeneracy loci

Fatighenti¹,

Meazzini²,

Mongardi³

et al. 2022

Preprint

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“…Most of the examples were found during the proof of Addendum 1.2. Example 5.3 and Example 5.5 were found starting from the configuration of lines communicated to the author by Degtyarev, using methods similar to the ones employed in [19].…”

Section: Examplesmentioning

confidence: 99%

“…There are 8 possible configurations with more than 52 lines, corresponding to 10 distinct surfaces. A list of explicit equations for these surfaces, initiated by Schur [12], Rams and Schütt [9], Degtyarev, Itenberg and Sertöz [5], and Shimada and Shioda [15], was completed by the author [19].…”

Section: Introductionmentioning

confidence: 99%

Lines on K3 quartic surfaces in characteristic 3

Veniani

2021

manuscripta math.

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We investigate the number of straight lines contained in a K3 quartic surface X defined over an algebraically closed field of characteristic 3. We prove that if X contains 112 lines, then X is projectively equivalent to the Fermat quartic surface; otherwise, X contains at most 67 lines. We improve this bound to 58 if X contains a star (ie four distinct lines intersecting at a smooth point of X). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided.

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