Downloads & Free Reading Options - Results

These notes are based upon my lectures at the Tata Institute from Novem- ber 1975 to March 1976 and further oral communication between me and the note taker. The notes are divided into two parts. In �8 or Part One we prove the Fundamental Theorem on the structure of the coordinate ring of a mero- morphic curve and its value group. We then give some applications of the Fundamental Theorem, the principal one among them being the Epimorphism Theorem. The proof of the Main Lemmas (� 7) presented here is a simplified version of the original proof of Abhyankar and Moh. The process of simplification started with my lectures at Poona Univer- sity in 1975 and culminated into the present version during my lectures at the Tata Institute. The simplification resulted mainly from the keen and stimulating interest in my lectures shown by the audience at these two places, especially at the Tata Institute. In Part Two we record some progress on the Jacobian problem, which is as yet unsolved. Lecture Notes Collection FreeScience.info ID2672 Obtained from http://www.math.tifr.res.in/~publ/ln/tifr57.pdf http://www.freescience.info/go.php?pagename=books&id=2672