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NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT
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Geometry-Algebra-Singularities-Combinatorics Seminar
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Enumerating singular curves on surfaces
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Steven L. Kleiman MIT
Northeastern University 509 Lake Hall 1:30 p.m., Monday, May 24, 1999
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Abstract: We'll discuss a nineteenth century problem of current interest: the enumeration of the r-nodal curves cut out of a smooth projective surface by the hypersurfaces of degree d. We require the curves to pass through enough points in general position so that the number of curves is finite. Then this number is given by an explicit universal polynomial in four basic Chern numbers, at least if r <= 8 and d>= 3r. A similar statement is true as well for the curves of any other equisingularity type. To justify the enumeration, we'll see that the curves of a given type form a reduced set of the expected dimension.
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Geometry-Algebra-Singularities-Combinatorics home page:
http://www.math.neu.edu/~suciu/GASC.html
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