Related papers: Coniveau 2 complete intersections and effective co…
We prove by induction on dimension the Hodge conjecture for smooth complex projective varieties. Let $X$ be a smooth complex projective variety. Then $X$ is birational to a possibly singular projective hypersurface, hence to a smooth…
We formulate and prove a B-model disc level large N duality result for general conifold transitions between compact Calabi-Yau spaces using degenerations of Hodge structures.
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
The aim of this survey is to explore complete intersection monomial curves from a contemporary perspective. The main goal is to help readers understand the intricate connections within the field and its potential applications. The…
The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the…
Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals I_A such that no binomial ideal contained in I_A and of the same dimension is a complete intersection. This result has…
We define the rigid homology. The trace morphism in rigid cohomology define by duality the cycle class in rigid homology. We verify the compatibility of this classes with rationnal equivalence and intersection theory. We deduce some formal…
We compute the cone of effective divisors on the Hilbert scheme of points in the projective plane. We show the sections of many stable vector bundles satisfy a natural interpolation condition, and that these bundles always give rise to the…
We study the common intersection of arrangements of double-wedges. We consider arrangements where double-wedges may be either bowties (which do not contain a vertical line) or hourglasses (which contain a vertical line), in contrast to…
We let R be a one-dimensional graded complete intersection, satisfying certain degree conditions which are satisfied whenever R is a numerical semigroup ring of embedding dimension at least three. We show that a graded maximal…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour $C$. For a special class of contours the gauge condition reduces to…
This paper aims to give some examples of diffeomorphic (or homeomorphic) low-dimensional complete intersections, which can be considered as a geometrical realization of classification theorems about complete intersections. A conjecture of…
Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. The main focus of this article is…
In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This…
This paper examines the feasible region of a standard conic program represented as the intersection of a closed convex cone and a set of linear equalities. It is recently shown that when Slater constraint qualification (strict feasibility)…
We compute explicitly the Chow motive of any generalized Kummer variety associated to any abelian surface. In fact, it lies in the rigid tensor subcategory of the category of Chow motives generated by the Chow motive of the underlying…
We describe an algorithm which verifies whether linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this confirms the integral Hodge conjecture for quartic and quintic Fermat…
In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture relating certain Hurwitz numbers (enumerating ramified coverings of the sphere) to the intersection theory on a conjectural Picard variety. We are going to use their…