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We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
Let $S$ be a smooth projective surface over a field. We introduce the notion of integral decomposability and, respectively, the opposite notion of integral indecomposability, of the transcendental motive $M^2_{\rm tr}(S)$. If the…
Let $X$ be either a general hypersurface of degree $n+1$ in $\mathbb P^n$ or a general $(2,n)$ complete intersection in $\mathbb P^{n+1}, n\geq 4$. We construct balanced rational curves on $X$ of all high enough degrees. If $n=3$ or $g=1$,…
In this paper we consider adjoint restriction estimates for space curves with respect to general measures and obtain optimal estimates when the curves satisfy a finite type condition. The argument here is new in that it doesn't rely on the…
The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the…
We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and non-orientable). We also give improved bounds for the topological complexity of unordered configuration spaces…
A $\sqrt{n}$ estimate in the hyperplane problem with arbitrary measures has recently been proved in \cite{K3}. In this note we present analogs of this result for sections of lower dimensions and in the complex case. We deduce these…
We investigate the convergence of entire Lagrange interpolations and of Hermite interpolations of exponential type in weighted $L^p$-spaces on the real line. The weights are reciprocals of entire functions and depend on the type and may be…
The construction of consistent effective field theories in the infrared demands that models be defined by their underlying gauge symmetries, rather than by an arbitrary tuning of couplings or a cherry-picking of operators which may not be…
We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.
We construct vast families of orthogonal operators obeying pentagon relation in a direct sum of three n-dimensional vector spaces. As a consequence, we obtain pentagon relations in Grassmann algebras, making a far reaching generalization of…
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…
This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two…
In this paper we establish effective lower bounds on the degrees of the Debarre and Kobayashi conjectures. Then we study a more general conjecture proposed by Diverio-Trapani on the ampleness of jet bundles of general complete intersections…
We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we establish a series of intersection theoretic inequalities, which we call rKT property, with…
The theory of relative logarithmic jet spaces is developed for log schemes. With this theory the existence of bounds of intersection multiplicities of curves and divisors on certain log schemes is established. This result extends those of…
Integrating hard constraints into deep learning is essential for safety-critical systems. Yet existing constructive layers that project predictions onto constraint boundaries face a fundamental bottleneck: gradient saturation. By collapsing…
A central problem in liaison theory is to decide whether every arithmetically Cohen-Macaulay subscheme of projective $n$-space can be linked by a finite number of arithmetically Gorenstein schemes to a complete intersection. We show that…
We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.
A relativistic theory constructed on Riemann-Cartan manifold with a derived totally antisymmetric torsion is proposed. It follows the coincidence of the autoparallel curve and metric geodesic. The totally antisymmetric torsion naturally…