B. Tighe

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math.AG2025

The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities

Benjamin Tighe

We extend results of Looijenga--Lunts and Verbitsky and show that the total Lie algebra $g$ for the intersection cohomology of a primitive symplectic variety $X$ with iso…

math.AG2024

The Holomorphic Extension Property for Higher Du Bois Singularities

Benjamin Tighe

Let $X$ be a normal complex variety and $I ¨ : X ~ \to X$ a resolution of singularities. We show that the inclusion morphism $I ¨ _{*} I^c ◯_{X ~}^{p} ↪ I^c ◯_{X}^{[p]}$ is an…

math.AG2024

Symmetries and vanishing theorems for symplectic varieties

Benjamin Tighe

We describe the local and Steenbrink vanishing problems for singular symplectic varieties with isolated singularities. We do this by constructing a morphism $$\mathbb D_X(\underlin…

math.AG2024

On an example of Aspinwall, Morrison, and SzendrÅi

Nicolas Addington, Benjamin Tighe

We study the cohomology of a 1-parameter family Y_t of Calabi-Yau 3-folds introduced by Aspinwall and Morrison, related to the mirror quintic family. SzendrÅi proved that Y_t, Y_{…

The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities

The Holomorphic Extension Property for Higher Du Bois Singularities

Symmetries and vanishing theorems for symplectic varieties

On an example of Aspinwall, Morrison, and SzendrÅi

On an example of Aspinwall, Morrison, and SzendrÅi