Annals of Mathematics

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• Non-quasi-projective moduli spaces AI翻译
  作者：Kollar, Janos
  摘要：We show that every smooth toric variety (and many other algebraic spaces as well) can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi-projective. This contradicts a recent paper (Quasi-projectivity of moduli spaces of polarized varieties, Ann. of Math. 159 (2004) 597-639.).
• Schubert induction AI翻译
  作者：Vakil, Ravi
  摘要：We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule of [V2]. As applications, we show that all Schubert problems for all Grassmannians are enumerative over the real numbers, and sufficiently large finite fields. We prove a generic smoothness theorem as a substitute for the Kleiman-Bertini theorem in positive characteristic. We compute the monodromy...
• The strong perfect graph theorem AI翻译
  作者：Chudnovsky, Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin
  摘要：A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. The strong perfect graph conjecture (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by Conforti, Cornuejols and Vuskovic-that every Berge graph either falls into one of a few basic classes...
• Logarithmic singularity of the Szego kernel and a global invariant of strictly pseudoconvex domains AI翻译
  作者：Hirachi, Kengo
• A preparation theorem for codimension-one foliations AI翻译
  作者：Loray, Frank
  摘要：After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension-one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for nondegenerate codimension-one foliations (proving in turn the analyticity), Strozyna-Zoladek for non degenerate planar vector fields and Bruno-Ecalle for saddle-node foliations in the plane.
• The equivariant Gromov-Witten theory of P1 AI翻译
  作者：Okounkov, A.; Pandharipande, R.
• Deligne's integrality theorem in unequal characteristic and rational points over finite fields AI翻译
  作者：Esnault, Helene
  摘要：If V is a smooth projective variety defined over a local field K with finite residue field, so that its etale cohomology over the algebraic closure K is supported in codimension 1, then the mod p reduction of a projective regular model carries a rational point. As a consequence, if the Chow group of 0-cycles of V over a large algebraically closed field is trivial, then the mod p reduction of a projective regular model carries a rational point.
• The partial derivativeb-complex on decoupled boundaries in Cn AI翻译
  作者：Nagel, Alexander; Stein, Elias M.
• Generalizations of the Poincare-Birkhoff theorem (vol 128, pg 139, 1988) AI翻译
  作者：Franks, John
• Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature AI翻译
  作者：Bethuel, F.; Orlandi, G.; Smets, D.
  摘要：For the complex parabolic Ginzburg-Landau equation, we prove that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen.