Facets of algebraic geometry : a collection in honor of William Fulton's 80th birthday (Volume 2)

"Let X be a complex nonsingular variety with globally generated tangent bundle. We prove that the signed Segre-MacPherson (SM) class of a constructible function on X with effective characteristic cycle is effective. This observation has a surprising number of applications to positivity questions in classical situations, unifying previous results in the literature and yielding several new results. We survey a selection of such results in this paper. For example, we prove general effectivity results for SM classes of subvarieties which admit proper (semi-)small resolutions and for regular or affine embeddings. Among these, we mention the effectivity of (signed) Segre-Milnor classes of complete intersections if X is projective and an alternation property for SM classes of Schubert cells in flag manifolds; the latter result proves and generalizes a variant of a conjecture of Feh'er and Rim'anyi. Among other applications we prove the positivity of Behrend's Donaldson-Thomas invariant for a closed subvariety of an abelian variety and the signed-effectivity of the intersection homology Chern class of the theta divisor of a non-hyperelliptic curve; and we extend the (known) nonnegativity of the Euler characteristic of perverse sheaves on a semi-abelian variety to more general varieties dominating an abelian variety"-- Provided by publisher Frontmatter 1 Dedication 5 Contents of Volume 2 7 Contents of Volume 1 9 Contributors (Volume 11 Contributors (Volume 1) 13 14 Stability of Tangent Bundles on Smooth Toric Picard-rank-2 Varieties and Surfaces 15 15 Tropical Cohomology with Integral Coefficients for Analytic Spaces 40 16 Schubert Polynomials, Pipe Dreams, Equivariant Classes, and a Co-transition Formula 77 17 Positivity Certificates via Integral Representations 98 18 On the Coproduct in Affine Schubert Calculus 129 19 Bost–Connes Systems and F1-structures in Grothendieck Rings, Spectra, and Nori Motives 161 20 Nef Cycles on Some Hyperk ̈ ahler Fourfolds 242 21 Higher Order Polar and Reciprocal Polar Loci 252 22 Characteristic Classes of Symmetric and Skew-symmetric Degeneracy Loci 268 23 Equivariant Cohomology, Schubert Calculus, and Edge Labeled Tableaux 298 24 Galois Groups of Composed Schubert Problems 350 25 A K-theoretic Fulton Class 381 Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field Written to honor the 80th birthday of William Fulton, the articles in this volume present substantial contributions to algebraic geometry, particularly combinatorial algebraic geometry and intersection theory. Covering a wide range of topics of current interest, the book will appeal to graduate students and established researchers in the field. Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry