Nilpotent orbits of a generalization of Hodge structures

By C. Hertling, Christian Sevenheck. 2006

82 citations recorded by the source corpus.

Abstract We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on ℙ1, with additional structure, a flat connection on ℂ*, a real subbundle and a pairing. We call these objects TERP-structures. We generalize to TERP-structures a correspondence of Cattani, Kaplan and Schmid between nilpotent orbits of Hodge structures and polarized mixed Hodge structures. The proofs use work of Simpson and Mochizuki on variations of twistor structures and a control of the Stokes structures of the poles at zero and infinity. The results are applied to TERP-structures which arise via oscillating integrals from holomorphic functions with isolated singularities.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/08843f04286973ca29cdcc394226427fe0263701

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hodge theoretic aspects of mirror symmetry (2008, background): “• A version of the notion of a (real) nc-Hodge structure appears in singularity theory in the work of Hertling [Her03, Her06] and Hertling-Sevenheck [HS07] under the name TER structure.”
Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules (2010, background): “ deﬁned by the pole of ∇ along z= 0 (in case it is irregular) is already deﬁned on the local system L, and not only on its complexiﬁcation L⊗R C was part of the deﬁnition of a mixed TERP-structure in [HS07]. It turns out that in some situations (see, e.g., [Moc08a, section 8]), this property is actu”
Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures (2014, background): “s in a recent progress [39,36] in physics on the sphere/hemisphere partition functions. Remark 1.5.1. In their studies of a ‘generalized’ Hodge structure (TERP/nc-Hodge structure), Hertling-Sevenheck [38] and Katzarkov-Kontsevich-Pantev [49] discussed the compatibility of the Stokes structure with t”
Limits of families of Brieskorn lattices and compactified classifying spaces (2008, background): “s called mixed if the tuple (H∞ arg6=0 ,(H ∞ arg6=0 )R,−N,S,Fe •) resp. (H∞ arg=0,(H ∞ arg=0)R,−N,S,Fe•) 7 is a polarized mixed Hodge structure of weight w−1 resp. of weight w. We refer to [Her03] or [HS07] for the notion of a polarized mixed Hodge structure (PMHS for short) used here. It is (Mz)s-i”