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Award ID contains: 1902743

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  1. ; (, Forum of Mathematics, Pi)
    Abstract In this paper, we determine the number of general points through which a Brill–Noether curve of fixed degree and genus in any projective space can be passed. 
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  2. ; ; (, International Mathematics Research Notices)
    Abstract Let $$\alpha \colon X \to Y$$ be a general degree $$r$$ primitive map of nonsingular, irreducible, projective curves over an algebraically closed field of characteristic zero or larger than $$r$$. We prove that the Tschirnhausen bundle of $$\alpha $$ is semistable if $$g(Y) \geq 1$$ and stable if $$g(Y) \geq 2$$. 
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  3. ; (, International Mathematics Research Notices)
    Abstract In this paper, we investigate an arithmetic analogue of the gonality of a smooth projective curve $$C$$ over a number field $$k$$: the minimal $$e$$ such that there are infinitely many points $$P \in C(\bar{k})$$ with $$[k(P):k] \leqslant e$$. Developing techniques that make use of an auxiliary smooth surface containing the curve, we show that this invariant can take any value subject to constraints imposed by the gonality. Building on work of Debarre–Klassen, we show that this invariant is equal to the gonality for all sufficiently ample curves on a surface $$S$$ with trivial irregularity. 
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  4. ; ; ; ; (, Research in Number Theory)
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  5. ; ; (, Algebra & Number Theory)
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  6. ; (, Research in the Mathematical Sciences)
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