scholarly journals Smoothing toroidal crossing spaces

2021 ◽  
Vol 9 ◽  
Author(s):  
Simon Felten ◽  
Matej Filip ◽  
Helge Ruddat
Keyword(s):  
Moduli Spaces ◽  
Frobenius Manifold ◽  
Compact Form ◽  
Homotopy Equivalence ◽  
Main Approach ◽  
Fano Manifolds ◽  
Normal Crossing ◽  
De Rham ◽  
Potential Applications ◽  
Infinitesimal Deformations

Abstract We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is to study log structures that are incoherent on a subspace of codimension 2 and prove a Hodge–de Rham degeneration theorem for such log spaces that also settles a conjecture by Danilov. We show that the homotopy equivalence between Maurer–Cartan solutions and deformations combined with Batalin–Vilkovisky theory can be used to obtain smoothings. The construction of new Calabi–Yau and Fano manifolds as well as Frobenius manifold structures on moduli spaces provides potential applications.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals Simple normal crossing Fano varieties and log Fano manifolds

2014 ◽  
Vol 214 ◽  
pp. 95-123
Author(s):  
Kento Fujita
Keyword(s):  
Fano Varieties ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Normal Crossing ◽  
Fano Index ◽  
Simple Normal Crossing

AbstractA projective log variety (X, D) is called alog Fano manifoldifXis smooth and ifDis a reduced simple normal crossing divisor onΧwith − (KΧ+D) ample. Then-dimensional log Fano manifolds (X, D) with nonzeroDare classified in this article when the log Fano indexrof (X, D) satisfies eitherr≥n/2withρ(X) ≥ 2 orr≥n− 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

scholarly journals The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

1997 ◽  
Vol 12 (06) ◽  
pp. 381-392 ◽  
Author(s):  
Mitsuko Abe
Keyword(s):  
Partition Function ◽  
Gravity Model ◽  
Moduli Spaces ◽  
Partition Functions ◽  
K3 Surface ◽  
Analytic Manifold ◽  
Rham Complex ◽  
De Rham ◽  
Complex Analytic Manifold ◽  
Equivalent Class

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein–Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some [Formula: see text]-torsions. [Formula: see text]-torsion is the extension of R-torsion for the de Rham complex to that for the [Formula: see text]-complex of a complex analytic manifold.

scholarly journals Simple normal crossing Fano varieties and log Fano manifolds

2014 ◽  
Vol 214 ◽  
pp. 95-123 ◽  
Author(s):  
Kento Fujita
Keyword(s):  
Fano Varieties ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Normal Crossing ◽  
Fano Index ◽  
Simple Normal Crossing

AbstractA projective log variety (X, D) is called a log Fano manifold if X is smooth and if D is a reduced simple normal crossing divisor on Χ with − (KΧ + D) ample. The n-dimensional log Fano manifolds (X, D) with nonzero D are classified in this article when the log Fano index r of (X, D) satisfies either r ≥ n/2 with ρ(X) ≥ 2 or r ≥ n − 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

scholarly journals Single-valued integration and double copy

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Francis Brown ◽  
Clément Dupont
Keyword(s):  
Moduli Spaces ◽  
Modular Forms ◽  
Differential Forms ◽  
Smooth Projective Variety ◽  
Genus Zero ◽  
Moduli Spaces Of Curves ◽  
Multiple Zeta ◽  
De Rham ◽  
Zeta Values ◽  
Double Copy

AbstractIn this paper, we study a single-valued integration pairing between differential forms and dual differential forms which subsumes some classical constructions in mathematics and physics. It can be interpreted as a p-adic period pairing at the infinite prime. The single-valued integration pairing is defined by transporting the action of complex conjugation from singular to de Rham cohomology via the comparison isomorphism. We show how quite general families of period integrals admit canonical single-valued versions and prove some general formulae for them. This implies an elementary “double copy” formula expressing certain singular volume integrals over the complex points of a smooth projective variety as a quadratic expression in ordinary period integrals of half the dimension. We provide several examples, including non-holomorphic modular forms, archimedean Néron–Tate heights on curves, single-valued multiple zeta values and polylogarithms. The results of the present paper are used in [F. Brown and C. Dupont, Single-valued integration and superstring amplitudes in genus zero, preprint 2019, https://arxiv.org/abs/1910.01107] to prove a recent conjecture of Stieberger which relates the coefficients in a Laurent expansion of two different kinds of periods of twisted cohomology on the moduli spaces of curves {\mathcal{M}_{0,n}} of genus zero with n marked points. We also study a morphism between certain rings of “motivic” periods, called the de Rham projection, which provides a bridge between complex periods and single-valued periods in many situations of interest.

Vanishing of Chern Classes of the De Rham Bundles for Some Families of Moduli Spaces

2007 ◽  
Vol 35 (5) ◽  
pp. 1525-1531 ◽  
Author(s):  
Indranil Biswas ◽  
Jaya Nn Iyer
Keyword(s):  
Moduli Spaces ◽  
Chern Classes ◽  
De Rham

scholarly journals Codimension one Fano distributions on Fano manifolds

2018 ◽  
Vol 20 (05) ◽  
pp. 1750058 ◽  
Author(s):  
Carolina Araujo ◽  
Mauricio Corrêa ◽  
Alex Massarenti
Keyword(s):  
Moduli Spaces ◽  
Projective Spaces ◽  
Complete Intersections ◽  
Picard Number ◽  
Contact Manifolds ◽  
Fano Manifolds ◽  
Codimension One ◽  
Linear Sections ◽  
Del Pezzo

In this paper, we investigate codimension one Fano distributions on Fano manifolds with Picard number one. We classify Fano distributions of maximal index on complete intersections in weighted projective spaces, Fano contact manifolds, Grassmannians of lines and their linear sections, and describe their moduli spaces. As a consequence, we obtain a classification of codimension one del Pezzo distributions on Fano manifolds with Picard number one.

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