Related papers: Homological projective duality for the Segre cubic
Let $X \subset \P^5_{\C}$ be a smooth cubic fourfold.The Kuznetsov component $\sA_X$ is contained in the derived category $D^b(X)$ and the transcendental motive $t(X)$ is contained in the category of Chow motives $\sM_{rat}(\C))$. If $X$…
EPW-sextics are special 4-dimensional sextic hypersurfaces (with 20 moduli) which come equipped with a double cover. We analyze the double cover of EPW-sextics parametrized by a certain prime divisor in the moduli space. We associate to the…
Let F be a polarized irreducible holomorphic symplectic fourfold, deformation equivalent to the Hilbert scheme parametrizing length-two zero-dimensional subschemes of a K3 surface. The homology group H^2(F,Z) is equipped with an integral…
We construct a self-dual complete resolution of a module defined by a pair of embedded complete intersection ideals in a local ring. Our construction is based on a gluing construction of Herzog and Martsinkovsky and exploits the structure…
We suggest a short proof of O.Benoist and O.Wittenberg theorem (arXiv:1907.10859) which states that for each real non-singular cubic hypersurface $X$ of dimension $\ge 2$ the real lines on $X$ generate the whole group $H_1(X(\Bbb R);\Bbb…
We compute the cohomological Hall algebra of zero-dimensional sheaves on an arbitrary smooth quasi-projective surface $S$ with pure cohomology, deriving an explicit presentation by generators and relations. When $S$ has trivial canonical…
The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be…
We show that four-dimensional superconformal algebras admit an infinite-dimensional derived enhancement after performing a holomorphic twist. The type of higher symmetry algebras we find are closely related to algebras studied by…
We discuss a connection between coherent duality and Verdier duality via a Gersten-type complex of sheaves on real schemes, and show that this construction gives a dualizing object in the derived category, which is compatible with the…
We extend non-emtpyness and irreducibility of Hassett divisors to the moduli spaces of $M$-polarizable cubic fourfolds for higher rank lattices $M$, which in turn provides a systematic approach for describing the irreducible components of…
We study two-dimensional holomorphic distributions on $\mathbb{P}^4$. We classify dimension two distributions, of degree at most $2$, with either locally free tangent sheaf or locally free conormal sheaf and whose singular scheme has pure…
In this paper, we examine holomorphic Segre preserving maps between the complexifications of real hypersurfaces in $\mathbb{C}^{n+1}$. In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…
In this paper, we study the higher codimensional cycle structure of the Hilbert scheme of three points in the projective plane. In particular, we compute all Chern (and Segre) classes of all tautological bundles on it and compute the nef…
The algebraic and geometric properties of a novel generalization of Clifford's classical C4 point-circle configuration are analysed. A connection with the integrable quaternionic discrete Schwarzian Kadomtsev-Petviashvili equation is…
In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology…
A desmic quartic surface is a birational model of the Kummer surface of the self-product of an elliptic curve. We recall the classical geometry of these surfaces and study their analogs in arbitrary characteristic. Moreover, we discuss the…
We construct a comultiplicative map on the projective bimodule resolution for a family of algebras one of which is cluster-tilted of type D4. The comultiplicative map is presented in terms of idempotents associated with vertices of the…
The symmetric group S_n possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of S_n itself, coincide with the irreducible representations of a certain algebra A_n.…