Interpolation for Restricted Tangent Bundles of General Curves
Interpolation for Restricted Tangent Bundles of General Curves
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发表时间：
2015
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通讯作者：
Eric Larson
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作者：
Eric Larson
Let (C, p_1, p_2, ldots, p_n) be a general marked curve of genus g, and q_1, q_2, ..., q_n in P^r be a general collection of points. We determine when there exists a nondegenerate degree d map f : C o P^r so that f(p_i) = q_i for all i. This is a consequence of our main theorem, which states that the restricted tangent bundle f^* T_{P^r} of a general curve of genus g, equipped with a general degree d map f to P^r, satisfies the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H^0(f^* T_{P^r}(-D)) = 0 or H^1(f^* T_{P^r}(-D)) = 0). We also prove an analogous theorem for the twist f^* T_{P^r}(-1).
