This research is in the area of algebraic geometry, more specifically Hodge theory and algebraic curves. In Hodge theory, Noether-Lefschetz theory, infinitesimal invariants of normal functions, the infinitesimal Abel-Jacobi map and the period map will be studied. In the theory of algebraic curves the relation between the minimal free resolution of a projective curve and the intrinsic geometry of the curve, especially which special divisors the curve carries will be studied. The two postdocs on the grant will work closely with the Principal Investigator. Cukierman will study the geometry of moduli spaces associated to algebraic curves. Wu will study infinitesimal invariants of normal functions. This work is in the very geometric side of algebraic geometry, that is it emphasizes the geometric and sometimes analytic side of the geometric objects defined by algebraic equations. This side of algebraic geometry tends to have applications throughout mathematics.
