Admissible Homomorphism And The Coherent Sheaves Categories Of Weighted Projective Lines Of Tubular Types

A weighted projective line consists of a sequence ?=(?1,?2,…,?t)of pairs of t different numbers in the projective line Pi(k)and a weight sequence p=(p1,p2,…,pt).The weight sequence determines an abelian group L(p)of rank 1,called the string group.The weighted projective line X(p,?)determines the L(p)-graded homogeneous coordi-nate algebra S(p,?).The coherent sheaves category coh-X(p,?)is the quotient abelian category mod L(p)-S(p,?)/mod0L(p)-S(p,?),where mod L(p)-S(p,?)is the abelian catego-ry of finitely generated L(p)-graded S(p,?)-modules and mod0L(p)-S(p,?)is the abelian category of finite dimension L(p)-graded S(p,?)-modules.In order to study the correlation of the coherent sheaves categories of weighted pro-jective lines,the paper[1]gives the definition of the admissible homomorphisms between string groups.The admissible homomorphism ?:L(p)?L(q)induces an equivalence of categories(coh-X(p,?))ker??coh-X(q,?).where(coh-X(p,?))ker? is the equivariant category which is induced by the group ker?.This paper studies the admissible homomorphisms between the string groups of tubu-lar types.Chapter 1 reca ll the development history of coherent sheaves categories over the weighted projective lines,and introduce the background of this thesis.Chapter 2 recall the relevant basic knowledge.Chapter 3 gives the complete classification of admis-sible homomorphisms of tubular types.Chapter 4 describe the correlation of the coherent sheaves categories of weighted projective lines of tubular types according to the admissible homomorphisms.