相关论文: Discriminant coamoebas through homology
This paper deals with coamoebas, that is, images under coordinatewise argument mappings, of certain quite particular plane algebraic curves. These curves are the zero sets of reduced A-discriminants of two variables. We consider the…
The amoeba of a complex curve in the 2-dimensional complex torus is its image under the projection onto the real subspace in the logarithmic scale. The complement to an amoeba is a disjoint union of connected components that are open and…
The microphase separated morphology of a melt of a specific class of comb-coil diblock copolymers, consisting of an AB comb block and a linear homopolymer A block, is analyzed in the weak segregation limit. On increasing the length of the…
We show that the closure of the coamoeba of a linear space/hyperplane complement is the union of products of coamoebas of hyperplane complements coming from flags of flats, and relate this to the Bergman fan. Using the Horn-Kapranov…
We give a new construction of cyclic homology of an associative algebra A that does not involve Connes' differential. Our approach is based on an extended version of the complex \Omega A, of noncommutative differential forms on A, and is…
We describe the relationship between dimer models on the real two-torus and coamoebas of curves in (\CC^\times)^2. We show, inter alia, that the dimer model obtained from the shell of the coamoeba is a deformation retract of the closed…
We construct a cycle in higher Hochschild homology associated to the 2-dimensional torus which represents 2-holonomy of a non-abelian gerbe in the same way the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary…
Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter-Drinfel'd distributive law between the comonad given…
The monodromy of torus bundles associated to completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article we…
We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result…
Consider a partial flag variety $X$ which is not a grassmaninan. Consider also its cohomology ring ${\rm H}^*(X,\ZZ)$ endowed with the base formed by the Poincar\'e dual classes of the Schubert varieties. In \cite{Richmond:recursion}, E.…
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…
We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…
We study the topology of complements of caustics of function singularities of low codimensions, in particular 1) complete the enumeration of connected components of the complements of caustics of {\em simple} (in the sense of V.Arnold)…
We adapt the notion of an algebraic theory to work in the setting of quasicategories developed recently by Joyal and Lurie. We develop the general theory at some length. We study one extended example in detail: the theory of commutative…
The paper deals with singularities of nonconfluent hypergeometric functions in several variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We describe such…
Let $B$ be a commutative algebra and $A$ be a $B$-algebra (determined by an algebra homomorphism $\varepsilon:B\rightarrow A$). M. D. Staic introduced a Hochschild like cohomology $H^{\bullet}((A,B,\varepsilon);A)$ called secondary…
Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…
Over the complex numbers, the complement of a collection of hyperplanes is a widely-studied object; the cohomology ring, in particular, is known to have a structure depending only on the combinatorial properties of the intersection of…