Intersections of entire curves and algebraic cycles on semi-abelian (40')
speaker: Junjiro Noguchi (University of Tokyo)abstract: In his monograph, “Introduction to Transcendental Numbers”Lang raised a problem that 1) an analytic 1-parameter subgroup of an abelian variety should have a non-empty intersection with an ample divisor, and 2) if the subgroup has Zariski dense image, the intersection should be infinite. The problem part 1) was affirmatively by J. Ax 6 years late, and the problem was extended for entire holomorphic curves (affirmative by Siu-Yeung, Noguchi). On the other hand, part 2) had been unknown for long time. We will discuss this problem from the view point of Nevanlinna theory of entire curves with respect to algebraic cycles of general codimension, and its Diophantine analogue motivated by Erd\"os' problem. (Joint with Winkelmann, Yamanoi, Corvaja.)
timetable:
Wed 26 Sep, 11:20 - 12:00, Sala Conferenze Centro De Giorgi
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