Let A be a finitary hereditary abelian category with enough projectives.We study the Hall algebra of complexes of fixed size over projectives.Explicitly,we first give a relation between Hall algebras of complexes of f...Let A be a finitary hereditary abelian category with enough projectives.We study the Hall algebra of complexes of fixed size over projectives.Explicitly,we first give a relation between Hall algebras of complexes of fixed size and cyclic complexes.Second,we characterize the Hall algebra of complexes of fixed size by generators and relations,and relate it to the derived Hall algebra of A.Finally,we give the integration map on the Hall algebra of 2-term complexes over projectives.展开更多
Let Md be the moduli space of stable sheaves on P2with Hilbert polynomial dm+1.In this paper,we determine the effective and the nef cone of the space Md by natural geometric divisors.Main idea is to use the wall-cross...Let Md be the moduli space of stable sheaves on P2with Hilbert polynomial dm+1.In this paper,we determine the effective and the nef cone of the space Md by natural geometric divisors.Main idea is to use the wall-crossing on the space of Bridgeland stability conditions and to compute the intersection numbers of divisors with curves by using the Grothendieck-Riemann-Roch theorem.We also present the stable base locus decomposition of the space M6.As a byproduct,we obtain the Betti numbers of the moduli spaces,which confirm the prediction in physics.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11801273)Natural Science Foundation of Jiangsu Province of China(Grant No.BK20180722)。
文摘Let A be a finitary hereditary abelian category with enough projectives.We study the Hall algebra of complexes of fixed size over projectives.Explicitly,we first give a relation between Hall algebras of complexes of fixed size and cyclic complexes.Second,we characterize the Hall algebra of complexes of fixed size by generators and relations,and relate it to the derived Hall algebra of A.Finally,we give the integration map on the Hall algebra of 2-term complexes over projectives.
基金supported by TJ Park Science Fellowship of POSCO TJ Park Foundation and National Research Foundation of Korea(Grant No.2013R1A1A2006037)
文摘Let Md be the moduli space of stable sheaves on P2with Hilbert polynomial dm+1.In this paper,we determine the effective and the nef cone of the space Md by natural geometric divisors.Main idea is to use the wall-crossing on the space of Bridgeland stability conditions and to compute the intersection numbers of divisors with curves by using the Grothendieck-Riemann-Roch theorem.We also present the stable base locus decomposition of the space M6.As a byproduct,we obtain the Betti numbers of the moduli spaces,which confirm the prediction in physics.
