Related papers: Quasi-BPS categories for K3 surfaces

We define and compute higher rank analogs of Pandharipande-Thomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani \cite{shesh1,shesh2}…

For various 2-Calabi-Yau categories $\mathscr{C}$ for which the stack of objects $\mathfrak{M}$ has a good moduli space $p\colon\mathfrak{M}\rightarrow \mathcal{M}$, we establish purity of the mixed Hodge module complex…

Using methods of stable homotopy theory, the category of symmetric quasi-coherent sheaves associated with non-commutative graded algebras with extra symmetries is introduced and studied in this paper. It is shown to be a closed symmetric…

We provide topological classification of possible phases with the symmetry of the planar phase of superfluid $^3$He. Compared to the B-phase (class DIII in classification of Altland and Zirnbauer), it has an additional symmetry, which…

The name "K3 surfaces" was coined by A. Weil in 1957 when he formulated a research programme for these surfaces and their moduli. Since then, irreducible holomorphic symplectic manifolds have been introduced as a higher dimensional analogue…

A geometric stack is a quasi-compact and semi-separated algebraic stack. We prove that the quasi-coherent sheaves on the small flat topology, Cartesian presheaves on the underlying category, and comodules over a Hopf algebroid associated to…

We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring $A$, with submetric (norm-decreasing) $A$-module homomorphisms for morphisms. If $A$ is a…

Let $S$ be a Riemann surface obtained by deleting a finite number of points, called cusps, from a compact Riemann surface. Let $\rho: \pi_1(S)\to Sl(n, \mathbb{C})$ be a semisimple linear representation of $\pi_1(S)$ which is unipotent near…

We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible…

This paper studies stable sheaves on abelian surfaces of Picard number one. Our main tools are semi-homogeneous sheaves and Fourier-Mukai transforms. We introduce the notion of semi-homogeneous presentation and investigate the behavior of…

We shall study some moduli spaces of Bridgeland's semi-stable objects on abelian surfaces and K3 surfaces with Picard number 1. Under some conditions, we show that the moduli spaces are isomorphic to the moduli spaces of Gieseker…

We consider modular properties of nodal curves on general $K3$ surfaces. Let $\mathcal{K}_p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\geqslant 3$ and $\mathcal{V}_{p,m,\delta}\to \mathcal{K}_p$ be the…

For a very general polarized $K3$ surface $S\subset \mathbb{P}^g$ of genus $g\ge 5$, we study the linear system on the Hilbert square $S^{[2]}$ parametrizing quadrics in $\mathbb{P}^g$ that contain $S$. We prove its very ampleness for…

We define a type B analogue of the category of finite sets with surjections, and we study the representation theory of this category. We show that the opposite category is quasi-Grobner, which implies that submodules of finitely generated…

We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by…

We study triple covers of K3 surfaces, following Miranda's theory of triple covers. We relate the geometry of the covering surfaces with the properties of both the branch locus and the Tschirnhausen vector bundle. In particular, we classify…

For infinitely many $d$, Hassett showed that special cubic fourfolds of discriminant $d$ are related to polarized K3 surfaces of degree $d$ via their Hodge structures. For half of the $d$, each associated K3 surface $(S,L)$ canonically…

In a recent article Halpern-Leistner defines the notion of quasi--convergent path in the space of Bridgeland stability conditions. Such a path induces a semiorthogonal decomposition of the derived category. We investigate quasi-convergent…

We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…

A K3 category is by definition a Calabi-Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no…