Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/9809172

Strongly homotopy algebras of a Kähler manifold

S. A. Merkulov
View original source ↗Read source document ↗Export metadata ↓

Abstract

It is shown that any compact Kähler manifold $M$ gives canonically rise to two strongly homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one with the Hodge theory of the Dolbeault complex. In these algebras the product of two harmonic differential forms is again harmonic. If $M$ happens to be a Calabi-Yau manifold, there exists a third strongly homotopy algebra closely related to the Barannikov-Kontsevich extended moduli space of complex structures.

Explore related subjects

math.AGmath.ATmath.DGmath.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. A. Merkulov. 2001-08-13. Strongly homotopy algebras of a Kähler manifold. https://arxiv.org/abs/math/9809172

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

KEEP EXPLORING

Related papers

arXiv2026

Shrinking dynamic on multidimensional tropical series

Let $Ω\subset\mathbb R^n$ be a compact convex domain. An $Ω$-tropical series is a nonnegative, concave, integral-slope, piecewise-affine function on $Ω$ that vanishes on $\partialΩ$. For a finite set $P\subsetΩ^\circ$, we study the least such function above prescribed initial data whose corner locus contains $P$. It is obtained by repeatedly applying one-point shrinking operators $G_p$. We prove that every fair order of these operators stabilizes after finitely many nontrivial steps. We also describe an event-driven implementation that records the lowest monomials at each point and updates only affected watcher lists. Finally, we show that, on every compact subset of $Ω^\circ$, the resulting dynamics can be approximated by a finite path whose intermediate tropical hypersurfaces have only mild singularities on that compact set; equivalently, the corresponding local cells of the dual regular subdivision contain no lattice points other than their vertices.

math.AG↗
arXiv2026

A stacky $p$-adic Riemann--Hilbert correspondence on Hitchin-small locus

Let $C$ be an algebraically closed perfectoid field over $\mathbb{Q}_p$ with the ring of integer $\mathcal{O}_C$ and the infinitesimal thickening $\Ainf$. Let $\mathfrak X$ be a semi-stable formal scheme over $\mathcal{O}_C$ with a fixed flat lifting $\widetilde{\mathfrak X}$ over $\Ainf$. Let $X$ be the generic fiber of $\mathfrak{X}$ and $\widetilde X$ be its lifting over $\BdRp$ induced by $\widetilde{\mathfrak X}$. Let $\MIC_r(\widetilde X)^{{\rm H}\text{-small}}$ and $\rL\rS_r(X,\BBdRp)^{{\rm H}\text{-small}}$ be the $v$-stacks of rank-$r$ Hitchin-small integrable connections on $X_{\et}$ and $\BBdRp$-local systems on $X_{v}$, respectively. In this paper, we establish an equivalence between these two stacks by introducing a new period sheaf with connection $(\calO\bB_{\dR,\pd}^+,\rd)$ on $X_{v}$.

math.AG↗
arXiv2026

A refinement of the coherence conjecture of Pappas and Rapoport

The coherence conjecture of Pappas and Rapoport, proved by Zhu, asserts the equality of dimensions for the global sections of a line bundle over a spherical Schubert variety in the affine Grassmannian and those of another line bundle over a certain union of Schubert varieties in a partial affine flag variety. We refine this equality of dimensions to an isomorphism of representations. The comparison is established by introducing a parahoric Bruhat-Tits group scheme $\mathcal{G}$ over the affine line, ramified at 0. We further strengthen this comparison by equipping any line bundle on the global Schubert variety of $\mathcal{G}$ with a unique equivariant structure under the global jet group scheme. As an application, we obtain new relations among affine Demazure modules.

math.AG↗