A construction of k-gonal curves with certain scrollar invariants
Received: 26 January 2001
Revised: 7 August 2001
Mathematics Subject Classification (2000): 14H51
Work partially supported by MURST and GNSAGA of INdAM (Italy)
Let X be a smooth projective curve of genus g ≥ 3 and R ∈ Pic k (X) with h 0(X,R)=2 and R spanned.
There are k-1 integers
ei 1 ≤ i ≤k-1, with e1 ≥ ... ≥ e k-1 ≥ 0 and e1 + ... +
e k-1=g-k+1 associated to R (the so-called scrollar invariants of R). Here il k is even we construct a
pair (X,R) such that the first k/2 scrollar invariants of R are k/2 prescribed integers ci, 1 ≤ i ≤ k/2,
up to a twist, i.e. ei=ci+x for 1 ≤ i ≤k/2 and any x ∈Z, x>>0.