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Counting curves on singular surfaces.

By: Contributor(s): Publication details: Rio de Janeiro: IMPA, 2015.Description: video onlineSubject(s): Online resources:
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Let S be a smooth projective surface and L a line bundle. As is now well known, the number of r-nodal curves in the linear system |L| passing through he appropriate number of points on S can be expressed as a polynomial of degree r in the Chern numbers L 2 , KS · L, K2 S , and c2(S). There has recently been works by several authors (Ardila–Block, Liu–Osserman, Block–G¨ottsche) that attempt to find similar formulas in the case that S is a singular toric surface. I will discuss this work, and also initial recent work by Nødland in the case of weighted projective planes .
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Let S be a smooth projective surface and L a line bundle. As is now well known, the number of r-nodal curves in the linear system |L| passing through he appropriate number of points on S can be expressed as a polynomial of degree r in the Chern numbers L 2 , KS · L, K2 S , and c2(S). There has recently been works by several authors (Ardila–Block, Liu–Osserman, Block–G¨ottsche) that attempt to find similar formulas in the case that S is a singular toric surface. I will discuss this work, and also initial recent work by Nødland in the case of weighted projective planes .

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