相关论文: Le calcul de Schubert selon Schubert
We try to understand and justify Schubert Calculus the way Schubert did it.
Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the…
We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.
We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real.
A flexible unified framework for both classical and quantum Schubert calculus is proposed. It is based on a natural combinatorial approach relying on the Hasse-Schmidt extension of a certain family of pairwise commuting endomorphisms of an…
We establish a Schubert calculus for Bott-Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B.
Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously…
We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by…
We give a signed puzzle rule to compute Schubert coefficients. The rule is based on a careful analysis of Knutson's recurrence arXiv:math/0306304. We use the rule to prove polynomiality of the sums of Schubert coefficients with bounded…
We give a direct geometric proof of the quantum Monk's formula which relies only on classical Schubert calculus.
We describe a method to compute Hurwitz-Hodge integrals.
We single out some problems of Schubert calculus of subspaces of codimension 2 that have the property that all their solutions are real provided that the data are real. Our arguments explore the connection between subspaces of codimension 2…
We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.
We calculate the tangent cones at unity of Schubert varieties for $A_n$, where $n$ is less or equal to four. We state several conjectures for an arbitrary $n$.
This paper works out the versions of the classical Giambelli and Pieri formulas in the context of quantum cohomology of a complex Grassmannian.
Coping with ambiguity has recently received a lot of attention in natural language processing. Most work focuses on the semantic representation of ambiguous expressions. In this paper we complement this work in two ways. First, we provide…
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell typically involves more equations than variables. We present a novel primal-dual formulation…
One approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Through an identification of the cohomology ring of the type A full flag variety with the polytope ring of the…
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.