This paintings includes sections at the moduli areas of vector bundles. the 1st half tackles the category of vector bundles on algebraic curves. the writer additionally discusses the development and straightforward homes of the moduli areas of sturdy bundles. specifically Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant idea. the second one half facilities at the constitution of the moduli area of semistable sheaves at the projective airplane. the writer sketches life stipulations for sheaves of given rank, and Chern type and building rules within the common context of projective algebraic surfaces. Professor Le Potier presents a remedy of vector bundles that would be welcomed through skilled algebraic geometers and newcomers alike.
Read or Download Lectures on Vector Bundles (Cambridge Studies in Advanced Mathematics) PDF
Best Algebraic Geometry books
Fractal styles have emerged in lots of contexts, yet what precisely is a trend? How can one make special the constructions mendacity inside of items and the relationships among them? This booklet proposes new notions of coherent geometric constitution to supply a clean method of this commonly used box. It develops a brand new inspiration of self-similarity referred to as "BPI" or "big items of itself," which makes the sphere a lot more straightforward for individuals to go into.
The idea of elliptic curves is wonderful through its lengthy background and by means of the range of the equipment which have been utilized in its examine. This ebook treats the mathematics technique in its smooth formula, by using simple algebraic quantity thought and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the publication proceeds with an exposition of the geometry and the formal team of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and international fields.
This booklet introduces the speculation of modular kinds, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner thought; Hecke eigenforms and their mathematics houses; the Jacobians of modular curves and the Abelian kinds linked to Hecke eigenforms.
Extra info for Lectures on Vector Bundles (Cambridge Studies in Advanced Mathematics)