【摘 要】
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Let X be an arbitrary smooth irreducible complex projective curve, E → X a rank two vector bundle generated by its sections. The author first represents E as a
【机 构】
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School of Mathematical Sciences
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Let X be an arbitrary smooth irreducible complex projective curve, E → X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2, f},where D1, D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ Ho (X, [D1] |D2)is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 29 × d matrix WE whose zero space gives Im{Ho(X, [D1]) → Ho(X, [D1] |D1 )} Im{Ho(X, E) → Ho(X, [D2]) →H0(X, [D2] |D2)}. From this and Ho(X, E) = Ho(X, [D1]) Im{Ho(X, E) → Ho(X, [D2])},it is got in particular that dimHo(X, E) = deg(E) - rank(WE) + 2.
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