Related papers: Log Smooth Deformation Theory
The introduction is modified in the revised version. Also, many typos and errors were corrected. Let $W\to C$ be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed…
We study the descent behaviour of homotopy-theoretic properties of smooth complex affine surfaces under finite surjective morphisms. We first examine the Eilenberg-MacLane property and show, by means of an explicit counterexample, that it…
Let $X$ be a normal variety. Assume that for some reduced divisor $D \subset X$, logarithmic 1-forms defined on the snc locus of $(X, D)$ extend to a log resolution $\tilde X \to X$ as logarithmic differential forms. We prove that then the…
We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact…
Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…
The purpose of this note is to extend the divergences analyzed in a previous work by application of the Deformed Logarithm in its most general form. In a study on entropic divergences, we have analyzed the different forms of the deformed…
It is shown that a smooth global deformation of quartic double solids, i.e. double covers of $\mathbb P^3$ branched along smooth quartics, is again a quartic double solid without assuming the projectivity of the global deformation. The…
This is the second part of the paper "A degeneration of stable morphisms and relative stable morphisms", (math.AG/0009097). In this paper, we constructed the relative Gromov-Witten invariants of a pair of a smooth variety and a smooth…
We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main…
The celebrated Morlet-Burghelea-Lashof-Kirby-Siebenmann smoothing theory theorem states that the group $\mathrm{Diff}_\partial(D^n)$ of diffeomorphisms of a disc $D^n$ relative to the boundary is equivalent to…
Normal form theory is developed deeply for planar smooth systems but has few results for piecewise-smooth systems because difficulties arise from continuity of the near-identity transformation, which is constructed piecewise. In this paper,…
We develop the theory of "virtual morphisms" in logarithmic algebraic geometry, introduced by Howell. It allows one to give algebro-geometric meaning to various useful maps of topological spaces that do not correspond to morphisms of (log)…
Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on $X$ relative to $D$. These moduli spaces are compactified by studying…
In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.
This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and…
In this article we investigate the regularity properties of linear degenerations of flag varieties. We classify the linear degenerations of (partial) flag varieties that are smooth. Furthermore, we study the singular locus of irreducible…
The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…
We present a set-theoretic version of some basic dilation results of operator theory. The results we have considered are Wold decomposition, Halmos dilation, Sz. Nagy dilation, inter-twining lifting, commuting and non-commuting dilations,…
This paper presents a survey on formal moduli problems. It starts with an introduction to pointed formal moduli problems and a sketch of proof of a Theorem (independently proven by Lurie and Pridham) which gives a precise mathematical…
We study the twisted knot module for the universal deformation of an ${\rm SL}_2$-representation of a knot group, and introduce an associated $L$-function, which may be seen as an analogue of the algebraic $p$-adic $L$-function associated…