Related papers: The cone construction via intersection theory

We investigate some combinatorial properties of convex polytopes simple in edges. For polytopes whose nonsimple vertices are located sufficiently far one from another, we prove an analog of the Hard Lefschetz theorem. It implies Stanley's…

Let $S$ be a complex projective surface. Lefschetz originally proved Lefschetz $(1, 1)$--Theorem by studying a Lefschetz pencil of hyperplane sections of $S$ and the Abel--Jacobi mapping. In this paper, we attack Lefschetz $(1, 1)$--Theorem…

We prove an intersection formula for two plane branches in terms of their semigroups and key polynomials. Then we provide a strong version of Bayer's theorem on the set of intersection numbers of two branches and apply it to the logarithmic…

In this short note, we give a new sufficient condition for the existence of long cycles in graphs involving Fan-type degree condition and neighborhood intersection.

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…

The generic chaining method provides a sharp description of the suprema of many random processes in terms of the geometry of their index sets. The chaining functionals that arise in this theory are however notoriously difficult to control…

An attempt to come closer to a resolution of the Collatz conjecture is presented. The central idea is the formation of a tree consisting of positive odd numbers with number 1 as root. Functions for generating the tree from the root are…

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.

In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…

Two cycles on a projective variety over an algebraically closed field are shown to be rationally equivalent if and only if their difference equals a difference of complete intersections of a certain kind. Some of Bloch's conjectures for…

Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.

This paper constructs a graded-commutative, associative, differential Transverse Intersection Algebra TIA {on the torus (in any dimension) with its cubical decomposition by using a probabilistic wiggling interpretation. This structure…

Let $X$ be any smooth Deligne-Mumford stack with projective coarse moduli, and $Y$ be a smooth complete intersection in $X$ associated with a direct sum of semi-positive line bundles. We will introduce a useful and broad class known as…

Interactions between several features sometimes play an important role in prediction tasks. But taking all the interactions into consideration will lead to an extremely heavy computational burden. For categorical features, the situation is…

In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…

We construct explicit examples of algebraic cycles in \bar M_g (for large g congruent to 2 mod 4) and in M_2,20 (no bar) which are not in the tautological ring. In an appendix we give a general method for computing intersections in the…

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

We use slicing by nongeneric pencils of hypersurfaces and prove a new theorem of Lefschetz type for singular non compact spaces, at the homotopy level. As applications, we derive results on the topology of the fibres of polynomial functions…

We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and…

We give a theorem of Leray-Hirsch type for Chow groups and use it to study the Hogde and Grothendieck's standard conjectures for algebraic fiber bundles of Leray-Hirsch type. Morevoer, the Hodge conjecture for product varieties will also be…