Related papers: Matrix Factorisation of Morse-Bott functions

We provide an equivalence between the dg category of coherent matrix factorizations and a certain dg category of absolute singularities. As an application, we compute the l-adic cohomology of the dg category of coherent matrix…

Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on $X$ and $\mathcal{A}'$ on $Y$, respectively. Suppose also we are…

We study the homotopy category $\mathrm{hmf}(R,W)$ of matrix factorizations of non-zero elements $W\in R^\times$, where $R$ is an elementary divisor domain. When $R$ has prime elements and $W$ factors into a square-free element $W_0$ and a…

Let G be a split, simple, simply connected, algebraic group over Q. The degree 4, weight 2 motivic cohomology group of the classifying space BG of G is identified with Z. We construct cocycles representing the generator of this group, known…

We study polynomial functors of degree 2, called quadratic, with values in the category of abelian groups $Ab$, and whose source category is an arbitrary category $\C$ with null object such that all objects are colimits of copies of a…

Results due to Druel and Beauville show that the blowup of the intermediate Jacobian of a smooth cubic threefold X in the Fano surface of lines can be identified with a moduli space of semistable sheaves of Chern classes c_1=0, c_2=2, c_3=0…

We write out explicit proper Calabi-Yau structures, i. e. non-degenerate cyclic cocycles on the differential graded categories of matrix factorizations of regular functions with isolated critical points. The formulas involve the Kapustin-Li…

We present an improved construction of the fundamental matrix factorization in the FJRW-theory given in arXiv:1105.2903. The revised construction is coordinate-free and works for a possibly nonabelian finite group of symmetries. One of the…

Using a recent construction of Bezrukavnikov and Etingof we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = S_n, this…

Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\mathbf{\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of…

We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consisting of free modules with edges being classical matrix…

In previous work, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral…

A famous theorem of D. Orlov describes the derived bounded category of coherent sheaves on projective hypersurfaces in terms of an algebraic construction called graded matrix factorizations. In this article, I implement a proposal of E.…

This paper concerns homological mirror symmetry for the pair-of-pants surface (A-side) and the non-isolated surface singularity $xyz=0$ (B-side). Burban-Drozd classified indecomposable maximal Cohen-Macaulay modules on the B-side. We prove…

This is the first part of a project aimed at formalizing Rozansky-Witten models in the functorial field theory framework. Motivated by work of Calaque-Haugseng-Scheimbauer, we construct a family of symmetric monoidal $(\infty,3)$-categories…

Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…

In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…

From the classic work of Gohberg and Krein (1958), it is well known that the set of partial indices of a non-singular matrix function may change depending on the properties of the original matrix. More precisely, it was shown that if the…

We construct a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. We show that its critical loci consist of linear subspaces that split into isotropic and complex…

Superconformal indices of four-dimensional $\mathcal{N}=1$ gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an $SL(3,\mathbb{Z})$ and $SL(2,\mathbb{Z})\ltimes…