Qianyu Chen

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math.AG2026

Restrictions of mixed Hodge modules using generalized V-filtrations

Qianyu Chen, Bradley Dirks, Sebastian Olano

We study generalized $V$ -filtrations, defined by Sabbah, on $D$ -modules underlying mixed Hodge modules on $X \times A^{r}$ . Using cyclic covers, we compare these filt…

math.AG2026

Hodge theory of secant varieties

Qianyu Chen, Bradley Dirks, Sebastian Olano +1

We study the local cohomology modules for the secant variety of lines of a smooth projective variety $Y$ and for higher secant varieties of smooth projective curves. We show that t…

math.AG2025

Partial Cohomologically Complete Intersections via Hodge Theory

Qianyu Chen, Bradley Dirks, Sebastian Olano

Using Saito's theory of mixed Hodge modules, we study a generalization of Hellus-Schenzel's "cohomologically complete intersection" property. This property is equivalent to pervers…

math.AG2025

The minimal exponent of cones over smooth complete intersection projective varieties

Qianyu Chen, Bradley Dirks, Mircea MustaÅ£Ä

We compute the minimal exponent of the affine cone over a complete intersection of smooth projective hypersurfaces intersecting transversely. The upper bound for the minimal expone…

math.AG2024

V-filtrations and minimal exponents for locally complete intersection singularities

Qianyu Chen, Bradley Dirks, Mircea MustaÅ£Ä +1

We define and study a notion of minimal exponent for a locally complete intersection subscheme $Z$ of a smooth complex algebraic variety $X$ , extending the invariant defined by Sai…