Let S ⊂ CP 3 be ’almost any’ projective surface of degree ≥ 4. ClassicalNoether-Lefschetz theorem states that any curve C ⊂ S can be written as an intersectionC = S∩ S 0 where S 0 is some surface in CP 3. Grothendieck-Lefschetz theorem generalizesthis result for higher dimension.In this survey talk we will discuss these theorems and the corresponding results forvector bundles. We will study related aspects of vector bundles over hypersurfaces andcomplex projective spaces. Our emphasis will be on extendibility theorems and varioussplitting criterion for vector bundles.We will also mention some recent results and open problems. The talk should beaccessible to a graduate student.
School of Mathematical Sciences
NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050