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{\bigboldfont
Harvard-M.I.T. Algebraic Geometry Seminar}

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Effective Schottky problem
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{\bf 
SAMUEL GRUSHEVSKY
}

Harvard University

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Schottky problem is the question of determining which abelian
varieties are jacobians of Riemann surfaces. The problem was posed by
Schottky in 1880s, and solved by Shiota in 1986. However, Shiota's
solution is not effective in the sense that given an explicit abelian
variety, one cannot decide whether it is a jacobian or not. In this
talk we present a series of results yielding a decision process for
solving the Schottky problem.

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Using complex-analytic and algebraic geometric techniques for the
moduli space of Riemann surfaces, we are able to bound the degree of
the equations involved. Using recent progress on effective
Nullstellensatz, we eliminate the unknowns from the KP equation in
Shiota's solution, and then applying the degree bounds to the
resulting differential equation yields an effective way to solve the
Schottky problem.

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February 12, 2002

3:00 p.m.

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MIT Room 4-163
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