Inventiones mathematicae

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• Pluricanonical systems on algebraic varieties of general type AI翻译
  作者：Takayama, Shigeharu
  作者单位：University of Tokyo
• Toda lattice, cohomology of compact Lie groups and finite Chevalley groups AI翻译
  作者：Casian, Luis; Kodama, Yuji
  作者单位：University System of Ohio; Ohio State University
• Rigidity of invariant convex sets in symmetric spaces AI翻译
  作者：Kleiner, B; Leeb, B
  作者单位：University of Michigan System; University of Michigan; University of Munich
  摘要：The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.
• Finiteness of relative equilibria of the four-body problem AI翻译
  作者：Hampton, M; Moeckel, R
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.
• Rigid modules over preprojective algebras AI翻译
  作者：Geiss, Christof; Leclerc, Bernard; Schroeer, Jan
  作者单位：University of Bonn; Universidad Nacional Autonoma de Mexico; Universite de Caen Normandie
  摘要：Let Lambda be a preprojective algebra of simply laced Dynkin type Delta. We study maximal rigid Lambda-modules, their endomorphism algebras and a mutation operation on these modules. This leads to a representation-theoretic construction of the cluster algebra structure on the ring C[N] of polynomial functions on a maximal unipotent subgroup N of a complex Lie group of type Delta. As an application we obtain that all cluster monomials of C[N] belong to the dual semicanonical basis.
• Universal lattices and property tau AI翻译
  作者：Kassabov, Martin; Nikolov, Nikolay
  作者单位：Cornell University; University of Oxford
  摘要：We prove that the universal lattices - the groups G = SLd(R) where R = Z[x(1),..., x(k)], have property tau for d >= 3. This provides the first example of linear groups with t which do not come from arithmetic groups. We also give a lower bound for the tau-constant with respect to the natural generating set of G. Our methods are based on bounded elementary generation of the finite congruence images of G, a generalization of a result by Dennis and Stein on K-2 of some finite commutative rings a...
• Singular symplectic moduli spaces AI翻译
  作者：Kaledin, D; Lehn, M; Sorger, C
  作者单位：Johannes Gutenberg University of Mainz; Nantes Universite; Institut Universitaire de France; Nantes Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension >= 4 they do no admit projective symplectic resolutions.
• Four positive formulae for type A quiver polynomials AI翻译
  作者：Knutson, Allen; Miller, Ezra; Shimozono, Mark
  作者单位：University of California System; University of California Berkeley; Virginia Polytechnic Institute & State University
  摘要：We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton [BF99 ]. All four formulae are combinatorial, in the sense that they are expressed in terms of combinatorial objects of certain types: Zelevinsky permutations, lacing diagrams, Young tableaux, and pipe dreams (also known as rc-graphs). Three of our formulae are multiplicity-free and geometric, meaning that their summands have coefficient 1 and correspond bijectively to components of a torus-invar...
• An invariance principle for isotropic diffusions in random environment AI翻译
  作者：Sznitman, AS; Zeitouni, O
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Minnesota System; University of Minnesota Twin Cities; Technion Israel Institute of Technology; Technion Israel Institute of Technology
  摘要：We investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more, we prove an invariance principle as well as transience. Our methods also apply to questions of homogenization in random media.
• The Weyl groupoid of a Nichols algebra of diagonal type AI翻译
  作者：Heckenberger, I
  作者单位：Leipzig University
  摘要：The theory of Nichols algebras of diagonal type is known to be closely related to that of semi-simple Lie algebras. In this paper the connection between both theories is made closer. For any Nichols algebra of diagonal type invertible transformations are introduced, which remind one of the action of the Weyl group on the root system associated to a semi-simple Lie algebra. They give rise to the definition of a groupoid. As an application an alternative proof of classification results of Rosso,...