相关论文: The Hodge structure of semiample hypersurfaces and…

We develop an approach to calculating the cup and cap products on Hochschild cohomology and homology of curved algebras associated with polynomials and their finite abelian symmetry groups. For polynomials with isolated critical points, the…

We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence…

We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences…

We express total set of rational Gromov-Witten invariants of projective spaces via periods of variations of semi-infinite Hodge structure associated with their mirror partners.

We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a holomorphic symplectic form. Such manifolda are also known as complex manifolds of hyperkaehler type. We obtain that a complex manifold of hyperkaehler type is Mirror…

With the help of the theory of holomorphic and anti-holomorphic differentials, G. A. Jones [Chiral covers of hypermaps, Ars Math. Contemp. 8 (2015), 425-431] proved that every regular hypermap of a non-spherical type is covered by an…

Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also…

We associate to every divisorial (e.g. smooth) variety $X$ with only constant invertible global functions and finitely generated Picard group a $Pic(X)$-graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate…

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic…

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the…

The moduli spaces of flat $\mathrm{SL}_2$- and $\mathrm{PGL}_2$-connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a…

In a previous paper, the author introduced a Z-structure in quantum cohomology defined by the K-theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle…

We study the multiplicative structure of orbifold Hochschild cohomology in an attempt to generalize the results of Kontsevich and Calaque-Van den Bergh relating the Hochschild and polyvector field cohomology rings of a smooth variety. We…

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…

Dimer models provide a method of constructing noncommutative crepant resolutions of affine toric Gorenstein threefolds. In homological mirror symmetry, they can also be used to describe noncommutative Landau--Ginzburg models dual to…

We introduce a new notion, called quasi-holomorphic maps. These are real smooth maps equipped with a structure that imitates the singularities and singularity stratifications of holomorphic maps on the source and target manifolds, although…

Let $X$ be a compact Riemann surface, $\Sigma$ a finite set of points and $M = X\setminus \Sigma$. We study the $L^2$ cohomology of a polarized complex variation of Hodge structure on a Galois covering of the Riemann surface of finite type…

We construct a generalization of the variations of Hodge structures on Calabi-Yau manifolds. It gives a Mirror partner for the theory of genus=0 Gromov-Witten invariants

We compute the subgroup of the monodromy group of a generalized Kummer variety associated to equivalences of derived categories of abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that the subgroup…

We construct an example of a non-trivial homogeneous quasimorphism on the group of Hamiltonian diffeomorphisms of the two and four dimensional quadric hypersurfaces which is continuous with respect to both the $C^0$-metric and the Hofer…