Related papers: Blow-up in manifolds with generalized corners

In 2019, Abramovich--Temkin--Wlodarczyk and McQuillan used weighted blow-ups to obtain very fast and functorial algorithms for resolution of singularities in characteristic zero. Recently, Abramovich--Quek--Schober simplified the…

Using the degeneration formula and absolute/relative correspondence, one studied the change of Gromov-Witten invariants under blow-up for six dimensional symplectic manifolds and obtained closed blow-up formulae for high genus Gromov-Witten…

We construct an injective map from the set of holomorphic equivalence classes of neighborhoods $M$ of a compact complex manifold $C$ into ${\mathbb C}^m$ for some $m<\infty$ when $(TM)|_C$ is fixed and the normal bundle of $C$ in $M$ is…

We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by…

The main theme of this work is the development of complexity induced generalized frameworks for static cylindrical polytropes. We consider two different definitions of generalized polytopes with charged anisotropic inner fluid distribution.…

We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features to establish a simple but flexible method for constructing…

We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…

This paper is concerned with the existence of constant scalar curvature Kaehler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kaehler metrics. We also consider the…

We classify Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.

The current article studies certain problems related to complex cycles of holomorphic foliations with singularities in the complex plane. We focus on the case when polynomial differential one-form gives rise to a foliation by Riemann…

We consider the 1D cubic NLS on $\mathbb R$ and prove a blow-up result for functions that are of borderline regularity, i.e. $H^s$ for any $s<-\frac 12$ for the Sobolev scale and $\mathcal F L^\infty$ for the Fourier-Lebesgue scale. This is…

We study the formation of generic singularities of mean curvature flow by combining the different approaches, specifically the methods in studying blowup of nonlinear heat equations, the techniques used by the author and the collaborators…

On a compact complex manifold we study the behaviour of strong K\"ahler with torsion (strong KT) structures under small deformations of the complex structure and the problem of extension of a strong KT metric. In this context we obtain the…

The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of…

Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint arXiv:math.AG/0306221. That is, they focus on the fact that toric…

We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation. Next, we construct a smooth counterexample to show that…

In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a…

Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves. It aims to systematically address…

We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a…

This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. In particular, this paper answers an open question posed by Guckenheimer and Scheper [SIAM J. Appl. Dyn. Syst. 10-1…