Geometry of genus 8 Nikulin surfaces and rationality of their moduli

2015/09/10 by Alessandro Verra, Verra, Alessandro
Arts and Humanities · Mathematics · #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #North African History and Literature #math.AG #msc:14J28

paper · pdf · doi:10.48550/arxiv.1509.03364

19 pages

arxiv created 2015/09/10 · openalex publication_date 2015/09/10 · arxiv updated 2015/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a general complex Nikulin surface of genus 8, a geometric construction of S is given as follows. Consider a smooth 3-fold linear section T of the Grassmannian G(1,4) and the Hilbert scheme of rational normal sextic curves of T. In it consider the special family of sextics A which are also contained in the congruence of bisecant lines to a rational normal quartic curve of P⁴. We show that S is biregular to a quadratic section of T containing a sextic A. In particular A admits a 1-dimensional family of bisecant lines contained in G(1,4) and 8 of them are in S. This explicit construction is then used to prove that the moduli space of genus 8 Nikulin surfaces is rational.

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