Bücher von Ian Morrison

Aims Theaimofthisbookistoprovideaguidetoarichandfascinatings- ject: algebraic curves, and how they vary in families. The revolution that the ?eld of algebraic geometry has undergone with the introd- tion of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understandthebehaviorofcurvesinwaysthatsimplywerenotpos- ble a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving long-standing problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn't intended to be a de?nitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to - cus on examples and applications rather than on foundations. When discussing techniques we've chosen to sacri?ce proofs of some, even basic,results-particularlywherewecanprovideagoodreference- inordertoshowhowthemethodsareusedtostudymoduliofcurves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication.

Sam is a young witch having a hard time fitting in with the other students at witch school. Sam is different from the other girls in her class-she likes to play sports, wear boys clothes, and has a crush on one of the other students who just happens to be a girl. When it becomes time for Sam to perform her spell for final exams, things do not go as planned-and it sets off a fun and magical adventure for herself, her cat Miss Kitty Popcorn, and her cat's bestie Cheese the mouse! There's enough pressure on Sam at Witch school since she comes from a big family of amazing witches-luckily there's a newly magical cat and mouse by Sam's side to get her though all this mess-and to discover her own magical self!