Related papers: Double spinor Calabi-Yau varieties
We relate Nakajima Quiver Varieties (or, rather, their multiplicative version) with moduli spaces of perverse sheaves. More precisely, we consider a generalization of the concept of perverse sheaves: microlocal sheaves on a nodal curve X.…
We consider two varieties associated to a web of quadrics W in the projective space of dimension 7. One is the base locus and the second one is the double cover of the three dimensional projective space branched along the determinant…
The Stenzel space fourfold is a non-compact Calabi-Yau which is a higher dimensional analogue of the deformed conifold. We consider N = (1,1) type IIA, N = 1 M-theory and N = (2,0) type IIB compactifications on this Stenzel space, thus…
For any smooth complex projective surface $S$, we construct semistable refined Vafa-Witten invariants of $S$ which prove the main conjecture of arXiv:1810.00078. This is done by extending part of Joyce's universal wall-crossing formalism to…
Let $S$ be a smooth projective variety and $\Delta$ a simple normal crossing $\mathbb{Q}$-divisor with coefficients in $(0,1]$. For any ample $\mathbb{Q}$-line bundle $L$ over $S$, we denote by $\mathscr{E}(L)$ the extension sheaf of the…
We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…
We study the geometry of a birational map between an intersection of a web of quadrics in seven-dimensional complex projective space that contains a plane and the double octic branched along the discriminant of the web.
We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with…
In this article we consider a question: what is the relation between two Calabi-Yau manifolds of two different Berglund--Hubsch types if they appear as hyper--surfaces in the quotient of the same weighted projective space. We show that that…
Using complexified quaternions, an intriguing link between generators of two different and surprisingly commuting four-dimensional representations of the SU(2)xU(1) Lie group, and generators of two four-dimensional spin 1/2 representations…
We state several questions, and prove some partial results, about the Chow ring $A^\ast(X)$ of complete intersections in projective space. For one thing, we prove that if $X$ is a general Calabi-Yau hypersurface, the intersection product…
We show that Koszul duality between differential graded categories and pointed curved coalgebras interchanges smooth and proper Calabi-Yau structures. This result is a generalization and conceptual explanation of the following two…
We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi--Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametrizing such deformations has…
We consider fibrations by abelian surfaces and K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain dual fibrations that are derived equivalent to the original fibration. Finally, we relate the problem to mirror…
This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…
We discuss the relation between the graded stable derived category of a hypersurface and that of its hyperplane section. The motivation comes from the compatibility between homological mirror symmetry for the Calabi-Yau manifold defined by…
We prove the existence of a canonical zero-cycle on a Calabi-Yau hypersurface X in a complex projective homogeneous variety. More precisely, we show that the intersection of any n divisors on X, n=dim X, is proportional to the class of a…
Given X a K3 surface, a mirror dual to X can be identified with a component of the moduli space of semistable sheaves on X. We consider fibrations by K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain a dual fibration…
In the first part of this paper, we obtain mirror formulas for twisted genus 0 two-point Gromov-Witten (GW) invariants of projective spaces and for the genus 0 two-point GW-invariants of Fano and Calabi-Yau complete intersections. This…
Generalizing the notions of reflexive polytopes and nef-partitions of Batyrev and Borisov, we propose a mirror symmetry construction for Calabi-Yau complete intersections in Fano toric varieties.