Symplectic structure of the moduli space of sheaves on an abelian or K3 surface

1984 ◽  
Vol 77 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Shigeru Mukai
Keyword(s):  
Moduli Space ◽  
Symplectic Structure ◽  
K3 Surface

scholarly journals Moduli spaces of stable vector bundles on Enriques surfaces

1998 ◽  
Vol 150 ◽  
pp. 85-94 ◽  
Author(s):  
Hoil Kim
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
K3 Surface ◽  
Enriques Surface ◽  
Stable Bundles ◽  
Stable Vector Bundles ◽  
Enriques Surfaces

Abstract.We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.

scholarly journals Lagrangian embeddings of cubic fourfolds containing a plane

2017 ◽  
Vol 153 (5) ◽  
pp. 947-972 ◽  
Author(s):  
Genki Ouchi
Keyword(s):  
Moduli Space ◽  
Derived Category ◽  
Lagrangian Submanifold ◽  
K3 Surface ◽  
Cubic Fourfold

We prove that a very general smooth cubic fourfold containing a plane can be embedded into an irreducible holomorphic symplectic eightfold as a Lagrangian submanifold. We construct the desired irreducible holomorphic symplectic eightfold as a moduli space of Bridgeland stable objects in the derived category of the twisted K3 surface corresponding to the cubic fourfold containing a plane.

The Moduli Space of Yang–Mills Connections Over a Compact Surface

1997 ◽  
Vol 09 (01) ◽  
pp. 77-121 ◽  
Author(s):  
Ambar Sengupta
Keyword(s):  
Explicit Formula ◽  
Moduli Space ◽  
Symplectic Structure ◽  
Compact Surface ◽  
Gauge Groups ◽  
Yang Mills

Yang–Mills connections over closed oriented surfaces of genus ≥1, for compact connected gauge groups, are constructed explicitly. The resulting formulas for Yang–Mills connections are used to carry out a Marsden–Weinstein type procedure. An explicit formula is obtained for the resulting 2-form on the moduli space. It is shown that this 2-form provides a symplectic structure on appropriate subsets of the moduli space.

The Euler number of certain primitive Calabi–Yau threefolds

2000 ◽  
Vol 128 (1) ◽  
pp. 79-86
Author(s):  
MEI-CHU CHANG ◽  
HOIL KIM
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Three Dimensional ◽  
Building Blocks ◽  
K3 Surfaces ◽  
Physical Models ◽  
Ample Divisor ◽  
K3 Surface ◽  
Superstring Theory ◽  
Two Parameters

Recently Calabi–Yau threefolds have been studied intensively by physicists and mathematicians. They are used as physical models of superstring theory [Y] and they are one of the building blocks in the classification of complex threefolds [KMM]. These are three dimensional analogues of K3 surfaces. However, there is a fundamental difference as is to be expected. For K3 surfaces, the moduli space N of K3 surfaces is irreducible of dimension 20, inside which a countable number of families Ng with g [ges ] 2 of algebraic K3 surfaces of dimension 19 lie as a dense subset. More explicitly, an element in Ng is (S, H), where S is a K3 surface and H is a primitive ample divisor on S with H2 = 2g − 2. For a generic (S, H), Pic (S) is generated by H, so that the rank of the Picard group of S is 1. A generic surface S in N is not algebraic and it has Pic (S) = 0, but dim N = h1(S, TS) = 20 [BPV]. It is quite an interesting problem whether or not the moduli space M of all Calabi–Yau threefolds is irreducible in some sense [R]. A Calabi–Yau threefold is algebraic if and only if it is Kaehler, while every non-algebraic K3 surface is still Kaehler. Inspired by the K3 case, we define Mh,d to be {(X, H)[mid ]H3 = h, c2(X) · H = d}, where H is a primitive ample divisor on a smooth Calabi–Yau threefold X. There are two parameters h, d for algebraic Calabi–Yau threefolds, while there is only one parameter g for algebraic K3 surfaces. (Note that c2(S) = 24 for every K3 surface.) We know that Ng is of dimension 19 for every g and is irreducible but we do not know the dimension of Mh,d and whether or not Mh,d is irreducible. In fact, the dimension of Mh,d = h1(X, TX), where (X, H) ∈ Mh,d. Furthermore, it is well known that χ(X) = 2 (rank of Pic (X) − h1(X, TX)), where χ(X) is the topological Euler characteristic of X. Calabi–Yau threefolds with Picard rank one are primitive [G] and play an important role in the moduli spaces of all Calabi–Yau threefolds. In this paper we give a bound on c3 of Calabi–Yau threefolds with Picard rank 1.

scholarly journals EPW cubes

2019 ◽  
Vol 2019 (748) ◽  
pp. 241-268 ◽  
Author(s):  
Atanas Iliev ◽  
Grzegorz Kapustka ◽  
Michał Kapustka ◽  
Kristian Ranestad
Keyword(s):  
Moduli Space ◽  
Hilbert Scheme ◽  
Symplectic Manifolds ◽  
K3 Surface ◽  
Degeneracy Loci ◽  
Double Covers ◽  
Formula Type

Abstract We construct a new 20-dimensional family of projective six-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 surface and are constructed as natural double covers of special codimension-three subvarieties of the Grassmannian G(3,6) . These codimension-three subvarieties are defined as Lagrangian degeneracy loci and their construction is parallel to that of EPW sextics, we call them the EPW cubes. As a consequence we prove that the moduli space of polarized IHS sixfolds of K3 -type, Beauville–Bogomolov degree 4 and divisibility 2 is unirational.

On Some Geometric Invariants Associated to the Space of Flat Connections on an Open Space

1996 ◽  
Vol 39 (2) ◽  
pp. 169-177
Author(s):  
I. Biswas ◽  
K. Guruprasad
Keyword(s):  
Moduli Space ◽  
Symplectic Structure ◽  
Open Space ◽  
Geometric Invariant ◽  
Flat Connections ◽  
Geometric Invariants ◽  
Marked Surface

AbstractA geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

scholarly journals ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES

2019 ◽  
Vol 62 (3) ◽  
pp. 640-660
Author(s):  
FLORIAN BOUYER
Keyword(s):  
Galois Group ◽  
Moduli Space ◽  
Monodromy Group ◽  
K3 Surfaces ◽  
K3 Surface ◽  
Field Of Definition ◽  
Irreducible Components ◽  
Definition Of

AbstractIn [5], Eklund showed that a general (ℤ/2ℤ)4 -invariant quartic K3 surface contains at least 320 conics. In this paper, we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space of (ℤ/2ℤ)4-invariant quartic K3 surface with a certain marked conic has 10 irreducible components.

Sign in / Sign up

Export Citation Format

Share Document