R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Algebraicity via Dual Positive Cones
Hsueh-Yung Lin (National Taiwan University)
Abstract:
Let
be a compact Kähler manifold. The celebrated Kodaira embedding theorem asserts that if the Kähler cone of
contains a rational cohomology class, then
is projective. Instead of considering Kähler classes, we will study the algebraicity of
when
carries a 1-dimensional positive rational Hodge class. We will first discuss and formulate some precise problems (depending on the notion of positivity) then focus on the following results:
1) If the interior of the dual Kähler cone of
contains a rational class, then the Picard variety of
is projective.
2) If the interior of the dual pseudoeffective cone of a compact Kähler threefold
contains a rational class, then
is projective.
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