• Brill–Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree 

      Hoff, Michael; Knutsen, Andreas Leopold (Journal article; Peer reviewed, 2020)
      We explicitly construct Brill–Noether general K3 surfaces of genus 4, 6 and 8 having the maximal number of elliptic pencils of degrees 3, 4 and 5, respectively, and study their moduli spaces and moduli maps to the moduli ...
    • Global sections of twisted normal bundles of K3 surfaces and their hyperplane sections 

      Knutsen, Andreas Leopold (Journal article; Peer reviewed, 2020)
      Let S⊂Pg be a smooth K3 surface of degree 2g−2, g≥3. We classify all the cases for which h0(NS/Pg(−2))≠0 and the cases for which h0(NS/Pg(−2))<h0(NC/Pg−1(−2)) for C⊂Pg−1 a general canonical curve section of S.
    • Moduli of curves on Enriques surfaces 

      Knutsen, Andreas Leopold; Ciliberto, Ciro; Dedieu, Thomas; Galati, Concettina (Journal article; Peer reviewed, 2020)
      We compute the number of moduli of all irreducible components of the moduli space of smooth curves on Enriques surfaces. In most cases, the moduli maps to the moduli space of Prym curves are generically injective or dominant. ...
    • Moduli of non-standard Nikulin surfaces in low genus 

      Knutsen, Andreas Leopold; Lelli-Chiesa, Margherita; Verra, Alessandro (Journal article; Peer reviewed, 2020)
      Primitively polarized genus g Nikulin surfaces (S, M, H) are of two types, that we call standard and non-standard depending on whether the lattice embedding Z[H] ⊕⊥ N ⊂ Pic S is primitive. Here H is the genus g polarization ...
    • A note on Severi varieties of nodal curves on Enriques surfaces 

      Knutsen, Andreas Leopold; Ciliberto, Ciro; Dedieu, Thomas; Galati, Concettina (Journal article; Peer reviewed, 2020)
      Let |L| be a linear system on a smooth complex Enriques surface S whose general member is a smooth and irreducible curve of genus p, with L2 > 0, and let V|L|,δ(S) be the Severi variety of irreducible δ-nodal curves in ...
    • On moduli spaces of polarized Enriques surfaces 

      Knutsen, Andreas Leopold (Journal article; Peer reviewed, 2020)
      We prove that, for any g≥2, the étale double cover ρg:Eg→̂Eg from the moduli space Egof complex polarized genus g Enriques surfaces to the moduli space ̂Egof numerically polarized genus g Enriques surfaces is disconnected ...