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2018 Workshop on Bridging Statistics and Sheaves
2018 Workshop Bridging Statistics and Sheaves
2017/12/20
Over the past 15 years, applied topology has brought tools from traditionally pure areas of mathematics, such as algebraic topology and category theory,to applied mathematics and statistics, all while...
Euler Characteristics of Tautological Sheaves on Hilbert Schemes of Points
Euler Characteristics Tautological Sheaveas Hilbert Schemes of Points
2015/3/24
Professor Chern recruited geometers, physicists and combinatorists to work at Nankai Institute of Mathematics (now Chern Institute of Mathematics).
CURVATURES OF DIRECT IMAGE SHEAVES OF VECTOR BUNDLES AND APPLICATIONS
CURVATURES DIRECT IMAGE SHEAVES VECTOR BUNDLES APPLICATIONS
2018/4/19
Let p : X ! S be a smooth K¨ahler fibration and E ! X a Hermitian holomorphic vector bundle. As motivated by the work of Berdtsson([Bern09]), by using basic Hodge theory, we derive several general cur...
From etale $P_{+}$-representations to $G$-equivariant sheaves on $G/P$
From etale $P_{+}$-representations $G$-equivariant sheaves $G/P$ Number Theory
2012/6/21
Let $K/\mathbb Q_{p}$ be a finite extension with ring of integers $o$, let $G$ be a connected reductive split $\mathbb Q_{p}$-group of Borel subgroup $P=TN$ and let $\alpha$ be a simple root of $T$ in...
The classification of semi-stable plane sheaves supported on sextic curves
semi-stable sheaves moduli space sheaves supported on plane curves
2012/5/24
We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients m...
Algebraic tori as Nisnevich sheaves with transfers
Algebraic tori Nisnevich sheaves Algebraic Geometry
2011/9/20
Abstract: We relate R-equivalence on tori with Voevodsky's theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
Hilbert-Kunz theory for nodal cubics, via sheaves
Hilbert-Kunz theory nodal cubics sheaves
2011/1/20
Suppose B = F[x, y, z]/h is the homogeneous coordinate ring of a characteristic p degree 3 irreducible plane curve C with a node. Let J be a homogeneous (x, y, z)-primary ideal and n → en be the Hilbe...
Artin-Tate motivic sheaves with finite coefficients over a smooth variety
Artin-Tate motivic finite coefficients smooth variety
2011/2/22
We propose a construction of a tensor exact category Fm X of Artin–Tate motivic sheaves with finite coefficients Z/m over a smooth variety X (over a field K of characteristic prime to m) in terms of &...
Degenerating the Jacobian: the Néron Model versus Stable Sheaves
N´ eron model stable sheaf compactified Jacobians relative Picard functor
2011/1/21
We provide sufficient conditions for the line bundle locus in a family of compact moduli spaces of pure sheaves to be isomorphic to the N´eron model. The result applies to moduli spaces construc...
Fibre sequences and localization of simplicial sheaves
Fibre sequences simplicial sheaves
2010/11/24
In this paper, we provide criteria for fibre sequences of simplicial sheaves to be preserved by nullification. This generalizes a result of Berrick and Dror Farjoun and allows a better understanding o...
A Note on Singular Moduli Spaces of Sheaves on K3 Surfaces
Singular Moduli Spaces K3 Surfaces
2010/11/24
This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two...
We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks....
Toric plurisubharmonic functions and analytic adjoint ideal sheaves
Toric plurisubharmonic functions analytic adjoint ideal sheaves
2010/11/19
In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier...
Toward a Mackey formula for compact restriction of character sheaves
Mackey formula compact restriction character sheaves
2010/11/15
We generalize a result by Cunningham-Salmasian to a Mackey-type formula for the compact restriction of a semisimple perverse sheaf produced by parabolic induction from a character sheaf, under certai...
Leaves and trajectories for schemes. Application to the comparison of three classical sheaves over the differential spectrum
Leaves trajectories schemes classical sheaves the differential spectrum
2010/11/15
We define leaves and trajectories for schemes endowed with a vector field. With the help of these tools, we are able to give a geometrical interpretation and to generalize several results and constru...