**EDOARDO BALLICO**

*A construction of k-gonal curves with certain scrollar invariants*

**Pages:** 159-162

**Received:** 26 January 2001
**Revised: ** 7 August 2001
**Mathematics Subject Classification (2000):** 14H51

Work partially supported by MURST and GNSAGA of INdAM (Italy)

**Abstract**:
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
e_{i} 1 ≤ i ≤k-1, with e_{1} ≥ ... ≥ 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.
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