Related papers: Equivariant Euler characteristics and sheaf resolv…

We study Quot schemes of 0-dimensional quotients of sheaves on 3-folds $X$. When the sheaf $\mathcal{R}$ is rank 2 and reflexive, we prove that the generating function of Euler characteristics of these Quot schemes is a power of the…

Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…

We show that a bound of the Castelnuovo-Mumford regularity of any power of the ideal sheaf of a smooth projective complex variety $X\subseteq\mathbb{P}^r$ is sharp exactly for complete intersections, provided the variety $X$ is cut out…

In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two…

We determine all the equivariant Euler characteristics of the building for the general unitary group over a finite field.

We get new results (and rederive some know ones) on smooth surfaces in $\mathbb{R}^n$ by unifying several view points into a coherent general view. Namely, we show and use new relations of the evolute (caustic) with the curvature ellipse,…

We apply the Yau-Zaslow-Beauville method to compute the Euler characteristic of the generalized Kummer varieties attached to a complex abelian surface (a calculation also done by Goettsche and Soergel by different methods). It is related to…

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…

In this paper, we introduce a new class of $\ell$-adic sheaves, which we call quadratic $\ell$-adic sheaves, on connected unipotent commutative algebraic groups over finite fields. They are sheaf-theoretic enhancements of quadratic forms on…

In this paper, we study some cohomology groups and quadratic twists of elliptic curves, and apply Tate local duality and the results of Kramer-Tunnell on local norm cokernel to give a refined version of Yu's formula in the case of elliptic…

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the…

We define the equivariant degree and local degree of a proper $G$-equivariant map between smooth $G$-manifolds when $G$ is a compact Lie group and prove a local to global result. We show the local degree can be used to compute the…

We prove that every maximally nodal sextic surface\,(with 65 nodes) $X \subset \mathbb{P}_{\mathbb{C}}^3$ contains a symmetric half-even set of nodes of cardinality 35. It follows that the associated half-quadratic sheaf is the cokernel of…

The goal of this paper is to prove Riemann-Roch type theorems for Deligne-Mumford algebraic stacks. To this end, we introduce a "cohomology with coefficients in representations" and a Chern character, and we prove a…

We introduce orbifold Euler numbers for normal surfaces with Q-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov-Miyaoka-Yau type inequality. As a…

We study the singularities of algebraic difference equations on curves from the point of view of equivariant sheaves. We propose a definition for the formal local type of an equivariant sheaf at a point in the case of a reduced curve acted…

Let $W$ be a Weyl group, and let $\CT_W$ be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of $W$, and its weight lattice. The real locus $\CT_W(\R)$ is a smooth, connected, compact…

Generating functions for the number of commuting m-tuples in the symmetric groups are obtained. We define a natural sequence of ``orbifold Euler characteristics'' for a finite group G acting on a manifold X. Our definition generalizes the…

We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate…

We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…