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Award ID contains: 1664303

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  1. ; (, Communications in Algebra)
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  2. ; ; (, Bulletin of the London Mathematical Society)
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  3. ; ; (, Selecta Mathematica)
    null (Ed.)
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  4. ; (, Advances in Mathematics)
    null (Ed.)
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  5. ; ; ; ; (, Journal of Pure and Applied Algebra)
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  6. ; (, Revista Matemática Contemporânea)
    null (Ed.)
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  7. ; (, Abel symposia)
    Brill-Noether Theorems play a central role in the birational geometry of moduli spaces of sheaves on surfaces. This paper surveys recent work on the Brill-Noether problem for rational surfaces. In order to highlight some of the difficulties for more general surfaces, we show that moduli spaces of rank 2 sheaves on very general hypersurfaces of degree d in P3 can have arbitrarily many irreducible components as d tends to infinity. 
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  8. ; (, Nagoya Mathematical Journal)
    In this paper, we show that the cohomology of a general stable bundle on a Hirzebruch surface is determined by the Euler characteristic provided that the first Chern class satisfies necessary intersection conditions. More generally, we compute the Betti numbers of a general stable bundle. We also show that a general stable bundle on a Hirzebruch surface has a special resolution generalizing the Gaeta resolution on the projective plane. As a consequence of these results, we classify Chern characters such that the general stable bundle is globally generated. 
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