Related papers: On nonnegatively graded Weierstrass points

The locus of genus-two curves with n marked Weierstrass points has codimension n inside the moduli space of genus-two curves with n marked points, for n<=6. It is well known that the class of the closure of the divisor obtained for n=1…

Let $X$ be a smooth cubic threefold. By invoking ideas from Geometric Manin's Conjecture, we give a complete description of the main components of the Kontsevich moduli space of genus one stable maps $\overline{M}_{1,0}(X)$. In particular,…

The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric $(0,2)$-tensors. More precisely, we construct a family of generalized curvature measures…

We study a metric version of the simplicial volume on Riemannian manifolds, the Lipschitz simplicial volume, with applications to degree theorems in mind. We establish a proportionality principle and a product inequality from which we…

It was suggested on several occasions by Deligne, Drinfeld and Kontsevich that all the moduli spaces arising in the classical problems of deformation theory should be extended to natural "derived" moduli spaces which are always smooth in an…

We consider subvarieties $N$ of $\mathcal{M}_{g,n}$, the moduli space of genus $g$ Riemann surfaces with $n$ marked points, that are totally geodesic with respect to the Teichm\"uller metric. The Deligne-Mumford boundary of…

We determine de Weierstrass semigroup of a pair of certain rational points on the GK-curves. We use this semigroup to obtain two-point AG codes with better parameters than comparable one-point AG codes arising from these curves. These…

We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy ${\mathbb {R}} P^5$ has infinitely many path components. We also show that in each dimension $4k+1$ there are at least $2^{2k}$ homotopy ${\mathbb…

Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such…

We show that the Poincar\'e bundle gives a fully faithful embedding from the derived category of a curve of sufficiently high genus into the derived category of its moduli space of bundles of rank $r$ with fixed determinant of degree 1.…

In one of his last papers, Boris Weisfeiler proved that if modular semisimple Lie algebra possesses a solvable maximal subalgebra which defines in it a long filtration, then associated graded algebra is isomorphic to one constructed from…

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a…

We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-preserving affine transformations of the ambient space and the…

We compute the number of F_q-points on M_{4,n}, for n less than or equal to 3, and show that it is a polynomial in q, using a sieve based on Hasse-Weil zeta functions. As an application, we prove that the rational singular cohomology groups…

We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to $\IT^2$ compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper…

We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a 1-parameter noncommutative deformation to any projective rational surface with smooth anticanonical curve. The construction agrees with one…

We study the curvature of the moduli space M_g of curves of genus g with the Siegel metric induced by the period map. We give an explicit formula for the holomorphic sectional curvature of M_g along a Schiffer variation at a point P on the…

The main purpose of this paper is to give an explicit description of the moduli space of semistable sheaves of rank two on a stable curve C obtained by gluing two smooth curves at a point. We prove that the moduli space is irreducible and…

Let G be a finite group acting tamely on a proper reduced curve C over an algebraically closed field. We study the G-module structure on the cohomology groups of a G-equivariant locally free sheaf F on C, and give formulas of…

A simplified, user-friendly repackaging of the curvature estimates implied by the Seiberg-Witten equations is formulated in terms of the convex hull of the set of monopole classes. New results are also obtained concerning boundary cases of…