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Some Applications of Weighted Integral Formulas

By Elin Götmark


We estimate the degree of polynomial solutions of the Bézout equation by means of the Koszul complex, and nd explicit solutions by means of integral formulas. We also give an explicit proof of Briançon-Skoda's theorem by means of integral formulas. Next we construct integral formulas for sections of the line bundles of P n, which also gives rise to a Koppelman formula in P n. As an application we obtain some (known) vanishing theorems. Acknowledgements I want to thank my advisor Mats Andersson for his help and inspiration. I also want to thank my roommate and fellow graduate student Elizabeth Wulcan for interesting discussions. Thanks go also to Håkan Samuelsson

Year: 2010
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