Syzygies of Toric Varieties
Syzygies of toric varieties by Milena Hering A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mathematics) in The University of Michigan 2006 Doctoral Committee: Professor William E. Fulton, Chair Professor Robert K. Lazarsfeld Professor Karen E. Smith Associate Professor Mircea I. Mustat¸˘a Associate Professor James Tappenden OÎ paÔsomai tc Qritac MoÔsaic sugkatameignÔc, dÐstan suzugÐan. Never will I cease to mingle the Graces and the Muses, sweetest union. (Theban Elders. Euripides, Heracles [675]) c Milena Hering 2005 All Rights Reserved F¨ur Mama ii ACKNOWLEDGEMENTS I am thankful to my parents for providing me with curiosity and openness towards the world. I would like to thank my family, for their steady support and for believing in my choices. I would like to thank Arend Bayer for his encouragement and just for being there. I have also received a lot of support and smiles from the people around me in Ann Arbor: Alina Andrei, Tobias Berger, Catherine Dupuis, Tom Fiore, Jason Howald, Amy Kiefer, Bob Lonigro, Hannah Melia, Kamilah Neighbors, Abigail Ochberg and her family, Elen Oneal, Irina Portenko, Karen Rhea, Sue Sierra, Zach Teitler, Ju- lianna Tymoczko, Edward Yu, Cornelia Yuen and all my friends. I would like to thank especially Afsaneh Mehran for sharing my ups and downs and making the latter lighter to bear. I have benefited from classes or discussions with Alexander Barvinok, Linda Chen, Alessio Corti, Igor Dolgachev, Gavril Farkas, Sergej Fomin, Angela Gibney, Amit Khetan, Kriz Klosin, Alex K¨uronya, Diane Maclagan, Laura Matusevich, Afsaneh Mehran, Leonardo Mihalcea, Vangelis Mourokos, Minh Nguyen, Benjamin Nill, Jes- sica Sidman, Janis Stipins, P.
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