Facets of algebraic geometry II.: A Collection in Honor of William Fulton's 80th Birthday (London Mathematical Society Lecture Note Series)

Written to honor the 80th birthday of William Fulton, the articles collected in these volumes present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include: commutative algebra, representation theory, tropical geometry, moduli spaces, Schubert calculus, quantum cohomology. 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. "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." Sommario fornito dall'editore Frontmatter Dedication Contents of Volume 2 Contents of Volume 1 Contributors (Volume Contributors (Volume 1) 14 Stability of Tangent Bundles on Smooth Toric Picard-rank-2 Varieties and Surfaces 15 Tropical Cohomology with Integral Coefficients for Analytic Spaces 16 Schubert Polynomials, Pipe Dreams, Equivariant Classes, and a Co-transition Formula 17 Positivity Certificates via Integral Representations 18 On the Coproduct in Affine Schubert Calculus 19 Bost–Connes Systems and F1-structures in Grothendieck Rings, Spectra, and Nori Motives 20 Nef Cycles on Some Hyperk ̈ ahler Fourfolds 21 Higher Order Polar and Reciprocal Polar Loci 22 Characteristic Classes of Symmetric and Skew-symmetric Degeneracy Loci 23 Equivariant Cohomology, Schubert Calculus, and Edge Labeled Tableaux 24 Galois Groups of Composed Schubert Problems 25 A K-theoretic Fulton Class Written to honor the 80th birthday of William Fulton, the articles collected in this volume 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.