Related papers: Spin canonical rings of log stacky curves
We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve C, based on the theory of formal pseudodifferential operators. When C is a complex curve with Poincar\'e uniformization, we propose…
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for, and…
Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized…
In this paper, we initiate our investigation of log canonical models for the moduli space of curves with the boundary divisor $\a \d$ as we decrease $\a$ from 1 to 0. We prove that for the first critical value $\a = 9/11$, the log canonical…
The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the kappa classes on the moduli space of nonsingular genus g curves. In a series of steps, the stable quotient relations are rewritten in…
Hashimoto and Ueda determined the weights of generators of the graded ring of modular forms on the Cayley half-space of degree two. In this paper we describe explicit generators. We show that the graded ring can be generated by Eisenstein…
This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold $Y_5$ (a linear section of $\mathbb{G}r(2,5)$). It contains new proofs of classical facts about lines, conics and cubics on $Y_5$, and about…
Over a Cohen-Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module,…
Triangular modular curves are a generalization of modular curves that arise from quotients of the upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves also arise naturally as a source of Belyi maps with…
We introduce the class of weakly log canonical singularities, a natural generalization of semi-log canonical singularities. Toric varieties (associated to toric face rings, possibly non-normal or reducible) which have weakly (semi-) log…
A commutative ring R has finite rank r, if each ideal of R is generated at most by r elements. A commutative ring R has the r-generator property, if each finitely generated ideal of R can be generated by r elements. Such rings are closely…
We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.
In [BFMT17] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In…
This note gives the complete projective classification of rational, cuspidal plane curves of degree at least 6, and having only weighted homogeneous singularities. It also sheds new light on some previous characterizations of free and…
The space of marked commutative rings on n given generators is a compact metrizable space. We compute the Cantor-Bendixson rank of any member of this space. For instance, the Cantor-Bendixson rank of the free commutative ring on n…
We describe a new perspective on the intersection theory of the moduli space of curves involving both Virasoro constraints and Gorenstein conditions. The main result of the paper is the computation of a basic 1-point Hodge integral series…
We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative…
We introduce the moduli space of generic piecewise circular $n$-gons in the Riemann sphere and relate it to a moduli space of Legendrian polygons. We prove that when $n=2k$, this moduli space contains a connected component homeomorphic to…
For $g \ge 5$, we give a complete classification of the connected components of strata of abelian differentials over Teichm\"uller space, establishing an analogue of Kontsevich and Zorich's classification of their components over moduli…
Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…