Discriminant Polytopes, Chow Polytopes, and K-energy Asymptotics on Algebraic Curves
نویسنده
چکیده
LetX ↪→ P be a smooth, linearly normal algebraic curve. We show that the asymptotics of the Mabuchi energy are completely determined by the discriminant polytope and the Chow polytope of X . From this we deduce a new and entirely algebraic proof that the Mabuchi energy of the rational normal curve of degree d ≥ 2 is bounded below along all degenerations. We conclude that the Moser-Trudinger-Onofri inequality also holds along all degenerations with a uniform lower bound depending only on d. CONTENTS
منابع مشابه
Hyperdiscriminant Polytopes, Chow Polytopes, and Mabuchi Energy Asymptotics
Let X ↪→ P be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of (X,ωFS |X) restricted to the Bergman metrics is completely determined by the X-hyperdiscriminant of format (n− 1) and the Chow form of X . As a corollary it is shown that the Mabuchi energy is bounded from below for all degenerations in G if and only if the hyperdiscriminant polytope dominates the ...
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