Special scrolls whose base curve has general moduli

Abstract

Abstract. In this paper we study the Hilbert scheme of smooth, linearly normal, special scrolls under suitable assumptions on degree, genus and speciality.

Brill–Noether loci of stable rank-two vector bundles on a general curve

“…There are smooth, linearly normal, special scrolls S ⊂ P 5 of degree 9, speciality 1, sectional genus 3 with general moduli containing a unique special section Γ which is a genus 3 canonical curve (cf. [11,Thm. 6.1]).…”

“…Remark 3.15. In [5] we constructed components of Hilbert schemes parametrizing smooth, linearly normal, special scrolls S ⊂ P r , of degree d, genus g having the base curve with general moduli. Such components were constructed for any g ≥ 3, i ≥ 1 and for any d ≥ 7g−ǫ 2 − 2i + 2, 0 ≤ ǫ ≤ 1, ǫ ≡ g (mod 2), unless i = 2 where d ≥ 4g − 3 (cf.…”

“…Such components were constructed for any g ≥ 3, i ≥ 1 and for any d ≥ 7g−ǫ 2 − 2i + 2, 0 ≤ ǫ ≤ 1, ǫ ≡ g (mod 2), unless i = 2 where d ≥ 4g − 3 (cf. [5,Thm. 6.1]).…”

“…The general point of any such component corresponds to an unstable vector bundle on C (cf. [5,Rem. 6.3]).…”

On some components of Hilbert schemes of curves

“…Important connections between Hilbert schemes parametrizing k-linear spaces contained in complete intersections of hyperquadrics and intermediate Jacobians (cf. [22]) are worth to be mentioned, whereas in [8,9] the Hilbert schemes of projective scroll surfaces have been related with families of rank-2 vector-bundles as well as with moduli spaces of (semi)stable ones. Surjectivity of Gaussian-Wahl maps on curves with general moduli ( [15,16]) has deep reflections both on suitable Hilbert schemes of associated cones and on the extendability of such curves (especially in the K3-case).…”