arXiv subjects

Dario Weissmann

Publications and source records attributed to Dario Weissmann.

6 recordsLinked to original sources

arXiv2026

The Hitchin morphism for K-trivial varieties

We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the spectral base. In other words, a stronger version of the conjecture of Chen and Ng\^o holds for this class of varieties, which includes K-trivial varieties. As part of the proof, we slightly modify the construction of spectral covers to obtain normal spectral covers.

math.AG↗

arXiv2026

Stratifying moduli spaces of Higgs bundles and the Hitchin morphism

We study the behavior of slope-stability of reflexive twisted sheaves over a normal projective variety $X$ under pullback along a cover. Slope-stability is always preserved if the cover does not factor via a quasi-\'etale cover. Fixing the rank, there is one quasi-\'etale cover that checks whether a twisted sheaf remains slope-stable on all Galois covers, yielding a stratification of the moduli space of slope-stable Higgs-bundles. As an application, we determine the image of the Hitchin morphism restricted to the smallest closed stratum of the Dolbeault moduli space when $X$ is smooth. This allows us to determine the image of the Hitchin morphism from the Dolbeault moduli space when $X$ is a hyperelliptic or abelian variety in characteristic $p\ge0$. In particular, we show that Chen-Ng\^o's conjecture holds for hyperelliptic varieties in characteristic $0$.

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arXiv2025

There are no exotic compact moduli of sheaves on a curve

We study moduli of coherent sheaves of some given degree and positive rank on a curve. We show that there is only one nonempty open condition on families of sheaves that yields a universally closed adequate moduli space, namely, the one that recovers the classical moduli of slope semistable vector bundles.

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arXiv2023

Stratifying the moduli space of stable vector bundles by decomposition type

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at least 2 we obtain mostly sharp dimension estimates for these strata. As an application, we obtain a dimension estimate for the closure of the prime to p trivializable stable bundles in the moduli space of stable vector bundles.

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arXiv2023

A stacky approach to identifying the semistable locus of bundles

We show that the semistable locus is the unique maximal open substack of the moduli stack of principal bundles over a curve that admits a schematic moduli space. For rank $2$ vector bundles it coincides with the unique maximal open substack that admits a separated moduli space, but for higher rank there exist other open substacks that admit separated moduli spaces.

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arXiv2022

A functorial approach to the stability of vector bundles

On a normal projective variety the locus of $\mu$-stable bundles that remain $\mu$-stable on all Galois covers prime to the characteristic is open in the moduli space of Gieseker semi-stable sheaves. On a smooth projective curve of genus at least 2 this locus is big in the moduli space of stable bundles, i.e., its complement has codimension at least 2.

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