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Hurwitz-Brill-Noether theory via K3 surfaces and stability conditions

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arxiv 2505.19890 v2 pith:WG3TFMNZ submitted 2025-05-26 math.AG

Hurwitz-Brill-Noether theory via K3 surfaces and stability conditions

Gavril Farkas , Soheyla Feyzbakhsh , Andr\'es Rojas This is my paper
classification math.AG
keywords theorysurfacescurveshurwitz-brill-noetherellipticstabilitybridgelandbrill-noether
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We develop a novel approach to the Brill-Noether theory of curves endowed with a degree k cover of the projective line via Bridgeland stability conditions on elliptic K3 surfaces. We first develop the Brill-Noether theory on elliptic K3 surfaces via the notion of Bridgeland stability type for objects in their derived category. As a main application, we show that curves on elliptic K3 surfaces serve as the first known examples of smooth k-gonal curves which are general from the viewpoint of Hurwitz-Brill-Noether theory. In particular, we provide new proofs of the main non-existence and existence results in Hurwitz-Brill-Noether theory. Finally, using degree-k Halphen surfaces, we construct explicit examples of curves defined over number fields which are general from the perspective of Hurwitz-Brill-Noether theory.

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Cited by 2 Pith papers

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  1. Two New Extensions of Reider's Theorem on Algebraic Surfaces

    math.AG 2026-04 unverdicted novelty 7.0

    Reider-type inequalities imply nefness of dH-E on blow-ups of P^3 along surfaces and sharp ample cone estimates for Hilbert schemes of length-d subschemes via Bridgeland semistability chambers and the Bayer-Macri theorem.

  2. Transmission permutations and Demazure products in Hurwitz--Brill--Noether theory

    math.AG 2026-04 unverdicted novelty 6.0

    Transmission permutations on twice-marked curves compose via the Demazure product, unifying dimension bounds for Brill-Noether theory in symmetric and affine symmetric groups.