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Creators/Authors contains: "Haburcak, Richard"

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  1. ; (, International Mathematics Research Notices)
    Abstract The Brill–Noether loci $$\mathcal{M}^{r}_{g,d}$$ parameterize curves of genus $$g$$ admitting a linear system of rank $$r$$ and degree $$d$$. When the Brill–Noether number is negative, they are proper subvarieties of the moduli space of genus $$g$$ curves. We explain a strategy for distinguishing Brill–Noether loci by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill–Noether loci. Via an analysis of the stability of Lazarsfeld–Mukai bundles, we obtain new lifting results for line bundles of type $$g^{3}_{d}$$ that suffice to prove the maximal Brill–Noether loci conjecture in genus $$3$$–$19$, $22$, $23$, and infinitely many cases. 
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    Free, publicly-accessible full text available October 1, 2026
  2. ; ; ; ; ; ; (, Selecta Mathematica)
    Free, publicly-accessible full text available March 4, 2026