Related papers: On Hilb/Sym correspondence for K3 surfaces

We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.

In this paper, we give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying new relations in the tautological ring of the moduli space of 2-pointed…

We compute the genus zero family Gromov-Witten invariants for K3 surfaces using the topological recursion formula and the symplectic sum formula for a degeneration of elliptic K3 surfaces. In particular we verify the Yau-Zaslow formula for…

In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror symmetry for genus-zero one-point…

Let $G$ be a nontrivial finite subgroup of $\SL_n(\C)$. Suppose that the quotient singularity $\C^n/G$ has a crepant resolution $\pi\colon X\to \C^n/G$ (i.e. $K_X = \shfO_X$). There is a slightly imprecise conjecture, called the McKay…

All reduced descendent Gromov-Witten invariants of $K3$ and abelian surfaces in primitive curve classes can be calculated by the methods of \cite{BOPY,MPT}. To handle the imprimitive curve classes, a multiple cover formula was conjectured…

In this paper we show that there is a correspondence between some $K3$ surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show…

We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the…

We prove the KKV conjecture expressing Gromov-Witten invariants of K3 surfaces in terms of modular forms. Our results apply in every genus and for every curve class. The proof uses the Gromov-Witten/Pairs correspondence for K3-fibered…

We study the Abramovich--Vistoli moduli space of genus zero orbifold stable maps to [Sym^2 P^2], the stack symmetric square of P^2. This compactifies the moduli space of stable maps from hyperelliptic curves to P^2, and we show that all…

We compute the genus one family Gromov-Witten invariants of K3 surfaces for non-primitive classes. These calculations verify Gottsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two…

We determine the automorphism group of the Hilbert scheme of two points on a generic projective K3 surface of any polarization. We obtain in particular new examples of Hilbert schemes of points having non-natural non-symplectic…

We study the higher genus equivariant Gromov-Witten theory of the Hilbert scheme of n points of the plane. Since the equivariant quantum cohomology is semisimple, the higher genus theory is determined by an R-matrix via the Givental-Teleman…

We compute open GW invariants for $\mathcal{K}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}$, open orbifold GW invariants for $[\C^3/\Z_2]$, formulate an open crepant resolution conjecture and verify it for this pair. We show that open…

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and…

We prove that genus zero Gromov--Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus zero orbifold Gromov--Witten invariants of an appropriate root stack construction along the divisor.

We consider K-theoretic Gromov-Witten theory of root constructions. We calculate some genus $0$ K-theoretic Gromov-Witten invariants of a root gerbe. We also obtain a K-theoretic relative/orbifold correspondence in genus $0$.

We prove that the locus of Hilbert schemes of n points on a projective K3 surface is dense in the moduli space of irreducible holomorphic symplectic manifolds of that deformation type. The analogous result for generalized Kummer manifolds…

We propose a conjecture that relates some local Gromov-Witten invariants of some crepant resolutions of Calabi-Yau 3-folds with isolated singularities with some Donaldson-Thomas type invariants of the moduli spaces of representations of…

An example of potential density of rational points on the second punctual Hilbert scheme of certain K3 surfaces is treated in detail. This is an amplification of some remarks made by O'Grady and Oguiso.