Related papers: Reflexive modules on normal Gorenstein Stein surfa…
(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…
We classify all normal stable Horikawa surfaces with only $\mathbb{Q}$-Gorenstein smoothable log canonical singularities. Furthermore, we provide a criterion for their global $\mathbb{Q}$-Gorenstein smoothability and describe the boundary…
We introduce and study the maximal-variation locus in families and moduli spaces of projective curves, defined via conductor-level balancing of meromorphic differentials on the normalization. This notion captures precisely when the space of…
Dabholkar, Murthy and Zagier (DMZ) proved that there is a canonical decomposition of a meromorphic Jacobi form of integral index for $\mathrm{SL}(2, \mathbb{Z})$ with poles on torsion points into polar and finite parts, and showed that the…
There is a canonical identification, due to the author, of a convex real projective structure on an orientable surface of genus g and a pair consisting of a conformal structure together with a holomorphic cubic differential on the surface.…
We define degeneracy loci for vector bundles with structure group $G_2$, and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the…
Based on Teichm\"uller theory, we construct a degenerating family $\overline{Y}_g^{orb} \rightarrow \overline{M}_g^{orb}$ over the Deligne-Mumford compactification of the moduli space with the natural orbifold structure such that any…
We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies with the…
Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with…
A recent construction of Hacking relates the classification of stable vector bundles on a surface of general type with $p_g = 0$ and the boundary of the moduli space of deformations of the surface. In the present paper we analyze this…
We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko…
We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of $I$-Ulrich modules.
Over a noetherian ring, it is a classic result of Matlis that injective modules admit direct sum decompositions into injective hulls of quotients by prime ideals. We show that over a Cohen-Macaulay ring admitting a dualizing module,…
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…
In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on…
We study modular subspaces corresponding to two deformation functors associated to an isolated singularity X_0: the functor Def_{X_0} of deformations of X_0 and the functor Def^s_{X_0} of deformations with section of X_0. After recalling…
We discuss the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. This category allows for…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be…
We discuss contact invariant structures on the space of solutions of a third-order ordinary differential equation. Associated to any third-order differential equation modulo contact transformations, Chern introduced a degenerate conformal…
This paper contributes to the theory of singularities of meromorphic linear ODEs in traceless $2\times2$ cases, focusing on their deformations and confluences. It is divided into two parts: The first part addresses individual singularities…