Related papers: A remark on virtual orientations for complete inte…
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
After recalling several constructions of the moduli space of curves of genus zero by different people we give our alternative construction of the moduli space. This gives a simple description of the intersection ring of this space. We give…
To every local complete intersection ring one may associate a so-called generic hypersurface. In this paper we introduce rank varieties for modules and complexes over the generic hypersurface. The definition uses extension of scalars,…
The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces $\mathbb{P}^1 \times \mathbb{P}^1$, we investigate which sets…
A Kuranishi atlas is a structure used to build a virtual fundamental class on moduli spaces of $J$-holomorphic curves. They were introduced by McDuff and Wehrheim to resolve some of the challenges in this field. This paper completes the…
In this paper the author provides a generalization of classical linkage, i.e. linkage by a complete intersection, in a different context. Namely she looks at residuals in the scheme theoretic intersection of a rational normal surface or…
The intention of this article is to make an attempt of classification of transitive Lie algebroids and on this basis to construct a classifying space. The realization of the intention allows to describe characteristic classes of transitive…
In this paper we calculate the elliptic genus of certain complete intersections in products of projective spaces. We show that it is equal to the elliptic genus of the Landau-Ginzburg models that are, according to Hori and Vafa, mirror…
We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete…
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…
In this paper we describe all possible reduced complete intersection sets of points on Veronese surfaces. We formulate a conjecture for the general case of complete intersection subvarieties of any dimension and we prove it in the case of…
One of the goals of this paper is to prove that the index of intersection of two complex curves in a two-dimensional complex manifold tangent to each other at a common boundary point is positive. This is achieved via the construction of a…
We study the class of equimultiple modules. In particular, we prove several criteria for an equimultiple module to be a complete intersection and prove the openness of the equimultiple locus of an ideal module.
We give a new proof of Ciocan-Fontanine and Kim's wall-crossing formula relating the virtual classes of the moduli spaces of $\epsilon$-stable quasimaps for different $\epsilon$ in any genus, whenever the target is a complete intersection…
In this paper we give a classification of complete intersection vanishing ideals on parameterized sets of clutter type over finite fields.
Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…
In this paper, we propose a general framework for universal zero-shot goal-oriented navigation. Existing zero-shot methods build inference framework upon large language models (LLM) for specific tasks, which differs a lot in overall…
The aim of this note is to provide a concise introduction to so-called problems of unlikely intersections for (pure) Shimura varieties and to review the current state-of-the-art. In the process, we will touch upon more general settings and…