Keep Up With Latest Trending Papers. Computer Science, AI and more.Subscribe

Top Papers in Hodge theory

Share

Almost complex Hodge theory

We review the recent development of Hodge theory for almost complex
manifolds. This includes the determination of whether the Hodge numbers defined
by $\bar\partial$-Laplacian are almost complex, almo

More...

Share

A Leray Model for a Polymatroid with arbitrary Building Set

Hodge Theory for Polymatroids

Read More...

Share

Hodge theory, between algebraicity and transcendence

The Hodge theory of complex algebraic varieties is at heart a transcendental
comparison of two algebraic structures. We survey the recent advances bounding
this transcendence, mainly due to the introd

More...

Share

Hodge theory of Kloosterman connections

We construct motives over the rational numbers associated with symmetric
power moments of Kloosterman sums, and prove that their L-functions extend
meromorphically to the complex plane and satisfy a f

More...

Share

Hodge theory in combinatorics

George Birkhoff proved in 1912 that the number of proper colorings of a
finite graph G with n colors is a polynomial in n, called the chromatic
polynomial of G. Read conjectured in 1968 that for any g

More...

Share

Hodge Laplacians on graphs

This is an elementary introduction to the Hodge Laplacian on a graph, a
higher-order generalization of the graph Laplacian. We will discuss basic
properties including cohomology and Hodge theory. The

More...

Share

Statistical ranking and combinatorial Hodge theory

We propose a number of techniques for obtaining a global ranking from data
that may be incomplete and imbalanced -- characteristics almost universal to
modern datasets coming from e-commerce and inter

More...

Share

Twisted functoriality in nonabelian Hodge theory in positive characteristic

We establish the twisted functoriality in nonabelian Hodge theory in positive
characteristic.

Share

Hodge theory of classifying stacks

We compute the Hodge and de Rham cohomology of the classifying space BG
(defined as etale cohomology on the algebraic stack BG) for reductive groups G
over many fields, including fields of small chara

More...

Share

Hodge theory for tropical varieties

In this paper we prove that the cohomology of smooth projective tropical
varieties verify the tropical analogs of three fundamental theorems which
govern the cohomology of complex projective varieties

More...

Share

Introduction to Nonabelian Hodge Theory: flat connections, Higgs bundles and complex variations of Hodge structure

Lecture notes from the Concentrated Graduate Course preceding the Workshop on
Hodge Theory in String Theory at the Fields Institute in Toronto, November
11--15, 2013.

Share

Singular Hodge theory for combinatorial geometries

We introduce the intersection cohomology module of a matroid and prove that
it satisfies Poincar\'e duality, the hard Lefschetz theorem, and the
Hodge-Riemann relations. As applications, we obtain pro

More...

Share

Hodge theory of twisted derived categories and the period-index problem

We study the Hodge theory of twisted derived categories and its relation to
the period-index problem. Our main contribution is the development of a theory
of twisted Mukai structures for topologically

More...

Share

The Hodge theory of Soergel bimodules

We prove Soergel's conjecture on the characters of indecomposable Soergel
bimodules. We deduce that Kazhdan-Lusztig polynomials have positive
coefficients for arbitrary Coxeter systems. Using results

More...

Share

$p$-adic Hodge theory for Artin stacks

This work is devoted to the study of integral $p$-adic Hodge theory in the
context of Artin stacks. For a Hodge-proper stack, using the formalism of
prismatic cohomology, we establish a version of $p$

More...

Share

Substitution maps in the Robba ring

The purpose of this note is to ask several questions about substitution maps
in the Robba ring. These questions are motivated by p-adic Hodge theory and the
theory of p-adic dynamical systems. We prov

More...

Share

Filtered A-infinity structures in complex geometry

We prove a filtered version of the Homotopy Transfer Theorem which gives an
A-infinity algebra structure on any page of the spectral sequence associated to
a filtered dg-algebra. We then develop vario

More...

Share

Local combinatorial formula for Euler class of PL spherical fiber bundle

Note on local combinatorial formula for Euler class of PL spherical fiber bundle

Read More...

Share

The perverse filtration for the Hitchin fibration is locally constant

We prove that the perverse Leray filtration for the Hitchin morphism is
locally constant in families, thus providing some evidence towards the validity
of the $P=W$ conjecture due to de Cataldo, Hause

More...

Share

Standard conjectures for abelian fourfolds

Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type
for A. By combining this result with a theorem of Clozel we deduce that
numerical equivalence on A coincides with l-adic ho

More...

Share

More