Related papers: Minimal model program for projective morphisms bet…
In a previous work, we described the Minimal Model Program in the family of $\Qbb$-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we…
This paper resolves several outstanding questions regarding the Minimal Model Program for klt threefolds in mixed characteristic. Namely termination for pairs which are not pseudo-effective, finiteness of minimal models and the Sarkisov…
We construct reduction and wall-crossing morphisms between the moduli spaces of stable pairs as the coefficients vary, generalizing the earlier work of Ascher, Bejleri, Inchiostro and Patakfalvi which deals with the klt case. Along the…
The semistable minimal model program is a special case of the minimal model program concerning 3-folds fibred over a curve and birational morphisms preserving this structure. We classify semistable divisorial contractions which contract the…
We consider the inclusion of the space of algebraic (regular) maps between real algebraic varieties in the space of all continuous maps. For a certain class of real algebraic varieties, which include real projective spaces, it is well known…
We prove that the moduli spaces of n-pointed m-stable curves introduced in our previous paper have projective coarse moduli. We use the resulting spaces to run an analogue of the Hassett-Keel log minimal model program for the moduli space…
We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.
This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the…
In this note, we prove a Schwarz-Pick type lemma for minimal maps between negatively curved Riemannian surfaces. More precisely, we prove that if $f:M \to N$ is a minimal map with bounded Jacobian between two complete negatively curved…
A theorem of Lawson and Simons states that the only stable minimal submanifolds in complex projective spaces are complex submanifolds. We generalize their result to the cases of quaternionic and octonionic projective spaces. Our approach…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
In this article, we functorially associate definable sets to $k$-analytic curves, and definable maps to analytic morphisms between them, for a large class of $k$-analytic curves. Given a $k$-analytic curve $X$, our association allows us to…
The following well known open problem is answered in the negative: Given two compact spaces $X$ and $Y$ that admit minimal homeomorphisms, must the Cartesian product $X\times Y$ admit a minimal homeomorphism as well? A key element of our…
We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.
Let $f:(X,B)\to Z$ be a 3-fold extremal dlt flipping contraction defined over an algebraically closed field of characteristic $p>5$, such that the coefficients of $\{B\}$ are in the standard set $\{1-\frac 1n|n\in \mathbb N\}$, then the…
The Sarkisov Program studies birational maps between varieties that are end products of the Minimal Model Program (MMP) on nonsingular uniruled varieties. If X and Y are terminal Q-factorial projective varieties endowed with a structure of…
We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…
Let (X,L) be a quasi polarized pairs, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles K_X + rL for high rational…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…