Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.05857

Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity for Variations of Mixed Hodge Structure

Gregory Pearlstein·Chris Peters
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article, we prove a rigidity criterion for period maps of admissible variations of graded-polarizable mixed Hodge structure, and establish rigidity in a number of cases, including families of quasi-projective curves, projective curves with ordinary double points, the complement of the canonical curve in families of Kynev--Todorov surfaces, period maps attached to the fundamental groups of smooth varieties and normal functions.

Explore related subjects

math.AGmath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gregory Pearlstein, Chris Peters. 2020-09-12. Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity for Variations of Mixed Hodge Structure. https://doi.org/10.14231/ag-2024-019

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗