{"product_id":"the-practice-of-algebraic-curves-a-second-course-in-algebraic-geometry-paperback-softback-9781470479435","title":"The Practice of Algebraic Curves; A Second Course in Algebraic Geometry (Paperback \/ softback) 9781470479435","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Practice of Algebraic Curves\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Second Course in Algebraic Geometry\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDavid Eisenbud (Author), Joe Harris (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470479435\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 28 February 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e413 pages\u003cbr\u003e25.4 x 17.8 x 2.6 cm, 0.744 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis textbook provides readers with a working knowledge of the modern theory of complex projective algebraic curves. Also known as compact Riemann surfaces, such curves shaped the development of algebraic geometry itself, making this theory essential background for anyone working in or using this discipline. Examples underpin the presentation throughout, illustrating techniques that range across classical geometric theory, modern commutative algebra, and moduli theory.  The book begins with two chapters covering basic ideas, including maps to projective space, invertible sheaves, and the Riemann-Roch theorem. Subsequent chapters alternate between a detailed study of curves up to genus six and more advanced topics such as Jacobians, Hilbert schemes, moduli spaces of curves, Severi varieties, dualizing sheaves, and linkage of curves in 3-space. Three chapters treat the refinements of the Brill-Noether theorem, including applications and a complete proof of the basic result. Two chapters on free resolutions, rational normal scrolls, and canonical curves build context for Green's conjecture. The book culminates in a study of Hilbert schemes of curves through examples. A historical appendix by Jeremy Gray captures the early development of the theory of algebraic curves. Exercises, illustrations, and open problems accompany the text throughout.  The Practice of Algebraic Curves offers a masterclass in theory that has become essential in areas ranging from algebraic geometry itself to mathematical physics and other applications. Suitable for students and researchers alike, the text bridges the gap from a first course in algebraic geometry to advanced literature and active research.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eLinear series and morphisms to projective space\u003c\/li\u003e\n\u003cli\u003eThe Riemann-Roch theorem\u003c\/li\u003e\n\u003cli\u003eCurves of genus 0\u003c\/li\u003e\n\u003cli\u003eSmooth plane curves and curves of genus 1\u003c\/li\u003e\n\u003cli\u003eJacobians\u003c\/li\u003e\n\u003cli\u003eHyperelliptic curves and curves of genus 2 and 3\u003c\/li\u003e\n\u003cli\u003eFine moduli spaces\u003c\/li\u003e\n\u003cli\u003eModuli of curves\u003c\/li\u003e\n\u003cli\u003eCurves of genus 4 and 5\u003c\/li\u003e\n\u003cli\u003eHyperplane sections of a curve\u003c\/li\u003e\n\u003cli\u003eMonodromy of hyperplane sections\u003c\/li\u003e\n\u003cli\u003eBrill-Noether theory and applications to genus 6\u003c\/li\u003e\n\u003cli\u003eInflection points\u003c\/li\u003e\n\u003cli\u003eProof of the Brill-Noether theorem\u003c\/li\u003e\n\u003cli\u003eUsing a singular plane model\u003c\/li\u003e\n\u003cli\u003eLinkage and the canonical sheave of a singular curves\u003c\/li\u003e\n\u003cli\u003eScrolls and the curves they contain\u003c\/li\u003e\n\u003cli\u003eFree resolutions and canonical curves\u003c\/li\u003e\n\u003cli\u003eHilbert schemes\u003c\/li\u003e\n\u003cli\u003eAppendix A: A historical essay on some topics in algebraic geometry (by Jeremy Gray)\u003c\/li\u003e\n\u003cli\u003eHints to marked exercises\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52702518051096,"sku":"9781470479435","price":62.59,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-practice-of-algebraic-curves-a-second-course-in-algebraic-geometry-paperback-softback-9781470479435","provider":"Freshly Printed Books","version":"1.0","type":"link"}