arXiv subjects

Sebastián Torres

Publications and source records attributed to Sebastián Torres.

5 recordsLinked to original sources

arXiv2026

Brauer groups of resolved quiver moduli via gerbes

We show that the Brauer group of any resolution of singularities of the moduli space of semistable quiver representations is trivial. We do this by extending the quiver-curve dictionary, translating a proof of the analogous result by Biswas-Hogadi-Holla for moduli of vector bundles on a curve to the setting of moduli of quiver representations, giving an algebro-geometric proof. This gives a new proof of this triviality, first proved by Le Bruyn-Schofield, building on algebraic (resp. cohomological) vanishing results due to Saltman (resp. Colliot-Thélène-Sansuc). Reversing the logic, our approach gives a new algebro-geometric proof of these vanishing results.

math.AG↗

arXiv2026

Weighted projective degenerations of $\mathbb{P}^{n}$

We study weighted projective klt $\mathbb{Q}$-Gorenstein degenerations of projective space $\mathbb{P}^{n}$ and construct infinitely many new degenerations of projective space in any dimension. We also study in detail the deformations of arbitrary weighted projective threefolds. The rest of the paper provides several applications of the existence of degenerations of $\mathbb{P}^{n}$ and our methods apply to find many degenerations of $\mathbb{P}^{n}$ beyond just weighted projective spaces.

math.AG↗

arXiv2024

Rational surfaces with a non-arithmetic automorphism group

In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples $Y$ are Looijenga pairs, i.e., there is a connected singular nodal curve $D \subset Y$ such that $K_{Y} + D = 0$.

math.AG↗

arXiv2023

The BGMN conjecture via stable pairs

Let $C$ be a smooth projective curve of genus $g\ge2$ and let $N$ be the moduli space of stable rank $2$ vector bundles on $C$ of odd degree. We construct a semi-orthogonal decomposition of the bounded derived category of $N$ conjectured by Narasimhan and by Belmans, Galkin and Mukhopadhyay. It has two blocks for each $i$-th symmetric power of $C$ for $i=0,\ldots,g-2$ and one block for the $(g-1)$-st symmetric power. We conjecture that the subcategory generated by our blocks has a trivial semi-orthogonal complement, proving the full BGMN conjecture. Our proof is based on an analysis of wall-crossing between moduli spaces of stable pairs, combining classical vector bundles techniques with the method of windows.

math.AG↗

arXiv2023

Bott vanishing using GIT and quantization

A smooth projective variety $Y$ is said to satisfy Bott vanishing if $Ω_Y^j\otimes L$ has no higher cohomology for every $j$ and every ample line bundle $L$. Few examples are known to satisfy this property. Among them are toric varieties, as well as the quintic del Pezzo surface, recently shown by Totaro. Here we present a new class of varieties satisfying Bott vanishing, namely stable GIT quotients of $(\mathbb{P}^1)^n$ by the action of $PGL_2$, over an algebraically closed field of characteristic zero. For this, we use the work done by Halpern-Leistner on the derived category of a GIT quotient, and his version of the quantization theorem. We also see that, using similar techniques, we can recover Bott vanishing for the toric case.

math.AG↗