Geometry of moduli space of sheaves on del Pezzo surfaces via Maruyama transform

In this paper, we prove that the moduli space of stable pairs (or sheaves) on del Pezzo surface S is isomorphic to the Maruyama type transformation of a projective bundle of a quiver representation space.     

Morphism spaces in stable categories of Frobenius algebras

We present an explicit formula computing morphism spaces in the stable category of a Frobenius algebra.     

范畴中态射集星型序的若干研究

本文证得星型序的乘法性质、遗传性质及其在偏序下态射广义逆的从属性质，并将星序的Hartwig上确界定理推广到带有对合*的正性预加法范畴中．     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

Varieties with P3 = 3 and q = dim(X)

We prove that if X is a complex projective variety with P₃(X) = 3 and q(X) = dim(X), then X is birational to a bidouble cover of A(X). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geometric Formulation of Higher-Order Lagrangian Systems in Supermechanics

Using supervector fields along a morphism of graded manifolds, we study both the geometry of the tangent supermanifolds of an arbitrary order and k th-order ordinary differential superequations, in order to develop the higher-order Lagrangian formalism of supermechanics. In particular, we obtain, in this formalism, a generalization of Noether's theorem and its converse.     

Quotient morphisms, compositions, and Fredholm index

In this paper we define a composition between two quotient morphisms and prove a multiplication formula for the index of the composition of two Fredholm quotient morphisms. Using this formula and the fact that any linear relation can be seen as a quotient morphism, we obtain a multiplication formula for the index of the composition of two Fredholm linear relations.     

关于具有泛分解态射的广义Moore-

本文讨论预加法范畴中态射的广义Moore-Perurose逆．给出了具有泛分解态射的广义Moore-Penrose逆存在的几个充要条件,并把结果应用到环上的矩阵中．     

The Ker-Coker-sequence and its generalization in some classes of additive categories

We study the validity of the Snake Lemma (the existence and exactness of the Ker-Cokersequence) in a P-semi-abelian category. We also obtain a generalization of the Snake Lemma in a quasiabelian category.