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A transcendental approach to Kollars injectivity theorem
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تأليف
Osamu Fujino
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نحن نعالج مبرهنة كولار للحقن من النظرة التحليلية (أو الهندسة التفاضلية). بشكل أكثر دقة، نقدم شرطا خطوط الإنحناء الذي يشير إلى أحكام كولار للحقن الشعبية. يتم تصريح أساسنا لهذا المبرهنة للمخلوق الكاهلي المضغوط، ولكن دليلنا يستخدم مساحة الأشكال الهارمونية على مجموعة زاريسكي مناسبة مع قياس كاهلي مكتمل. لا نحتاج إلى الحيل التغطية، ولا التجزئة، ولا سلسلة اسكترال ليراي.
We treat Kollars injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature condition which implies Kollar type cohomology injectivity theorems. Our main theorem is formulated for a compact Kahler manifold, but the proof uses the space of harmonic forms on a Zariski open set with a suitable complete Kahler metric. We need neither covering tricks, desingularizations, nor Lerays spectral sequence.
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