اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAsymptotic expansion of the Bergman kernel via perturbation of the Bargmann-Fock model
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We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the $k$-th tensor powers of a positive line bundle $L$ in a $frac{1}{sqrt{k}}$-neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kahler potential $kvarphi$ in a $frac{1}{sqrt{k}}$-neighborhood of a given point, the potential becomes an asymptotic perturbation of the Bargmann-Fock metric. We then prove that the Bergman kernel is also an asymptotic perturbation of the Bargmann-Fock Bergman kernel.
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