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math.AG2002
Noether-Lefschetz for K_1 of a Surface, Revisited
Xi Chen, James D. Lewis
Let Z be a general surface in P^3 of degree at least 5. Using a Lefschetz pencil argument, we give an elementary new proof of the vanishing of a regulator on K_1(Z).
math.AG2001
On Algebraic Hyperbolicity of Log Varieties
Xi Chen
Fix a very general hypersurface D in P^n of degree at least 2n + 1 and we show that the complement P^n - D does not contain any algebraic torus C^*.
math.AG2001
On Algebraic Hyperbolicity of Log Surfaces
Xi Chen
We call a log variety (X, D) algebraically hyperbolic if there exists a positive number e such that 2g(C) - 2 + i(C, D) >= e deg(C) for all curves C on X, where i(C, D) is the numb…
math.AG2000
On the Intersection of Two Plane Curves
Xi Chen
We study the following question: fix a sufficient general curve D of degree d in P^2, what is the least number of intersections between D and an irreducible curve of degree m? G. X…