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Birational geometry of irreducible holomorphic symplectic tenfolds of O’Grady type
In this paper, we analyse the birational geometry of O’Grady ten dimensional manifolds, giving a characterization of Kähler classes and lagrangian...
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Supersingular Irreducible Symplectic Varieties
In complex geometry, irreducible holomorphic symplectic varieties, also known as compact hyper-Kähler varieties, are natural higher-dimensional...
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Curve Neighborhoods of Schubert Varieties in the Odd Symplectic Grassmannian
Let IG( k ,2 n + 1) be the odd symplectic Grassmannian. It is a quasi-homogeneous space with homogeneous-like behavior. A very limited description of...
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SYMPLECTIC PBW DEGENERATE FLAG VARIETIES; PBW TABLEAUX AND DEFINING EQUATIONS
We define a set of PBW-semistandard tableaux that is in a weight-preserving bijection with the set of monomials corresponding to integral points in...
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Unchaining surgery and topology of symplectic 4-manifolds
We study a symplectic surgery operation we call unchaining , which effectively reduces the second Betti number and the symplectic Kodaira dimension at...
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Toric Degenerations in Symplectic Geometry
Toric degeneration in algebraic geometry is a process of degenerating a given projective variety into a toric one. Then one can obtain information...
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Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds
Let 𝒪 be a closed orientable 2-orbifold of negative Euler characteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic form ω on...
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Rational curves on primitive symplectic varieties of OG\(_6^s\)-type
We prove that any ample class on a primitive symplectic variety that is a locally trivial deformation of O’Grady’s singular 6-dimensional example is...
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Symplectic Blowing Down in Dimension Six
We establish a blowing down criterion in the context of birational symplectic geometry in dimension 6.
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Singular symplectic spaces and holomorphic membranes
We set up a topological framework for degenerations of symplectic manifolds into singular spaces paying a special attention to the behavior of...
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Real simple symplectic triple systems
The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides...
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Elements of Symplectic Geometry
The first section of this chapter is a primer on symplectic algebra and geometry in Euclidean spaces, real or complex. Concepts and results are...
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Examples of Irreducible Symplectic Varieties
Irreducible symplectic manifolds are one of the three building blocks of compact Kähler manifolds with numerically trivial canonical bundle by the...
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Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution
Over the past 2 decades, there has been much progress on the classification of symplectic linear quotient singularities V / G admitting a symplectic...
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Minimal Rational Curves and 1-Flat Irreducible G-Structures
1-Flat irreducible G-structures, equivalently, irreducible G-structures admitting torsion-free affine connections, have been studied extensively in...
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Quantum cohomology as a deformation of symplectic cohomology
We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the...
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Deformations of symplectic singularities and orbit method for semisimple Lie algebras
We classify filtered quantizations of conical symplectic singularities and use this to show that all filtered quantizations of symplectic quotient...
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Symplectic Resolutions for Multiplicative Quiver Varieties and Character Varieties for Punctured Surfaces
We study the algebraic symplectic geometry of multiplicative quiver varieties, which are moduli spaces of representations of certain quiver algebras,...
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Quantum cohomology as a deformation of symplectic cohomology
We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the...