Related papers: Discriminant coamoebas through homology
We investigate the cohomology of the Milnor fibre of a reflection arrangement as a module for the group $\Gamma$ generated by the reflections, together with the cyclic monodromy. Although we succeed completely only for unitary reflection…
We define a new version of $\mathbb A^1$-homology, called cellular $\mathbb A^1$-homology, for smooth schemes over a field that admit an increasing filtration by open subschemes with cohomologically trivial closed strata. We provide several…
We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to…
Morita introduced in 2008 a 1-cocycle on the group of homology cobordisms of surfaces with values in an infinite-dimensional vector space. His 1-cocycle contains all the "traces" of Johnson homomorphisms which he introduced fifteen years…
We explain how homotopical information of two composeable relations can be organized in two simplicial categories that augment the relations row and column complexes. We show that both of these categories realize to weakly equivalent…
The global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard-Fuchs equation, the series expansions around large complex structure,…
Given a topological group $ G $ and a Hausdorff topological group $ A $ on which $ G $ acts continuously and compatibly with the group operation of $ A $, we study the set of continuous cocycles of $ G $ with value in $ A $. This set is a…
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up…
Let R=K[M] be a normal affine monoid algbera over a field K.Up to isomorphism the conic ideals are exactly the direct summands ofthe extension R^{1/n} of R. We show that the classes of the conic divisorial ideals can be identified with the…
We study $A$-hypergeometric systems $H_A(\beta)$ in the sense of Gelfand, Kapranov and Zelevinsky under two aspects: the structure of their holonomically dual system, and reducibility of their rank module. We prove first that rank-jumping…
We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure,…
Mirror symmetry of Calabi-Yau manifolds can be understood via a Legendre duality between a pair of certain affine manifolds with singularities called tropical manifolds. In this article, we study conifold transitions from the point of view…
The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and…
The integral cohomology ring of the complement of an arrangement of linear subspaces of a finite dimensional complex projective space is determined by combinatorial data, i.e. the intersection poset and the dimension function.
We begin with proving a formula relating the Hilbert series of a graded algebra $A$ and the Poincar\'{e} series for $A$ in two variables. This gives the Fr\"oberg formula in the case where the bigraded $Tor^A(k,k)$ is concentrated on the…
For a monotone symplectic manifold and a smooth anticanonical divisor, there is a formal deformation of the symplectic cohomology of the divisor complement, defined by allowing Floer cylinders to intersect the divisor. We compute this…
We introduce the notion of spaces with weak relative cohomology and show the acyclicity of the complement $Q\setminus X$ in the Hilbert cube $Q$ of a compactum $X$ with weak relative cohomology. As a corollary we obtain the acyclicity of…
A theory of higher colimits over categories of free presentations is developed. It is shown that different homology functors such as Hoshcshild and cyclic homology of algebras over a field of characteristic zero, simplicial derived…
We continue the B-model development of the open/closed correspondence proposed by Mayr and Lerche-Mayr, complementing the A-model study in the preceding joint works with Liu and providing a Hodge-theoretic perspective. Given a corresponding…
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…