Related papers: Minimal resolutions of threefolds
In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The…
A rational map between certain specific threefolds is given in an explicit manner.
We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie…
We study when Taylor resolutions of monomial ideals are minimal. We consider monomial ideals with linear quotients. In particular, we determine precisely the stable ideals and the monomial ideals with linear resolutions having the miminal…
We give necessary and sufficient conditions on the singular Bj\"{o}rling data to the singular Bj\"{o}rling problem's solution has a prescribed nature of singularity. As an application, we prove that near a maxface with a particular type of…
We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that…
Let U be a basepoint free four-dimensional subspace of the space of sections of O(2,1) on P^1 x P^1. The sections corresponding to U determine a regular map p_U: P^1 x P^1 --> P^3. We study the associated bigraded ideal I_U in k[s,t;u,v]…
With a view to study problems of smoothability, we construct a minimal free resolution for the coordinate ring of an algebroid monomial curve associated to an $AS$ numerical semigroup (i.e. generated by an arithmetic sequence), obtained…
This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…
We describe an explicit symplectic resolution for the quotient singularity arising from the four-dimensional symplectic represenation of the binary tetrahedral group.
For three dimensional complete Riemannian manifolds with scalar curvature no less than one, we obtain the sharp upper bound of complete stable minimal surfaces' diameter.
We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so-called special Picard curves over $\mathbb{Q}$ with good reduction outside 2 and 3, and use this to determine…
We provide a characterisation of all graphs whose parity binomial edge ideals have pure resolutions. In particular, we show that the minimal free resolution of a parity binomial edge ideal is pure if and only if the corresponding graph is a…
The philosophy of the article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of singularities. The idea is used in two related problems: (1) We give a proof of…
We consider the minimal entropy problem, namely the question of whether there exists a smooth metric of minimal entropy, for certain classes of 3-manifolds. Among other resulsts, we show that if M is a closed, orientable, geometrizable…
We describe the Taylor and Lyubeznik resolutions as simplicial resolutions, and use them to show that the Scarf complex of a monomial ideal is the intersection of all its minimal free resolutions.
Locally analytically, any isolated double point occurs as a double covering of a smooth surface. It can be desingularized via the canonical resolution, as it is well-known. In this paper we explicitly compute the fundamental cycle of both…
We prove a quantitative estimate on the number of certain singularities in almost minimizing clusters. In particular, we consider the singular points belonging to the lowest stratum of the Federer-Almgren stratification (namely, where each…
We describe a method for counting the number of $1$-connected trivalent $2$-stratifolds with a given number of singular curves and $2$-manifold components.
We investigate the existence of complete intersection threefolds $X \subset \mathbb{P}^n$ with only isolated, ordinary multiple points and we provide some sufficient conditions for their factoriality.