Constructions of K-Regular Maps Using Finite Local Schemes
Explore k-regular maps and interpolation theory in algebraic geometry. Learn construction methods, bounds, and applications to continuous function interpolation using advanced mathematical concepts.
Deformation Theory for Finite Cluster Complexes
Explore geometric relationships between cluster varieties and complexes, focusing on finite cluster types with universal coefficients and their connection to Hilbert schemes via torus actions.
A Geometric R-Matrix for the Hilbert Scheme of Points on a General Surface
Explore geometric R-matrices for Hilbert schemes of points on general surfaces, delving into advanced mathematical concepts and their applications.
Moduli Spaces of Sheaves and Vafa-Witten Formula in Algebraic Geometry
Explore moduli spaces of sheaves, Hilbert schemes, and the Vafa-Witten formula. Learn about perfect obstruction theories, virtual fundamental classes, and their role in defining enumerative invariants for singular spaces.
Hochschild Cohomology and Deformation Theory of Hilbert Schemes of Points on Surfaces
Explore Hochschild cohomology of Hilbert schemes, its impact on deformation theory, and connections to symmetric quotient stacks. Gain insights into twisted Hodge numbers and recent research developments.
Cohomology Rings of Character Varieties
Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.
Flops and Hilbert Scheme of Space Curve Singularities
Explore pagoda flop transitions and their application in deriving explicit results for topological invariants of Hilbert schemes of space curve singularities.
Wall-Crossing for Calabi-Yau Fourfolds and Applications
Explore wall-crossing formulae for Calabi-Yau fourfolds, their proof, and applications to stable pairs counting points, curves, and surfaces, building on Joyce's framework.
A Support Theorem for Nested Hilbert Schemes of Planar Curves
Explore nested Hilbert schemes of planar curves and their support theorem, delving into advanced mathematical concepts in algebraic geometry.
Soergel Bimodules, Matrix Factorizations and Hilbert Schemes
Explore Soergel bimodules, matrix factorizations, and Hilbert schemes in quantum topology, focusing on representation theory applications.
Kummer Extensions: Applications to Generalized Cross-Ratios and Functions on Hilbert Schemes
Explore Kummer extensions in geometry and arithmetic, including generalized cross-ratios and functions on Hilbert schemes. Gain insights into advanced algebraic geometry concepts.
Donaldson-Thomas Invariants: Classical, Motivic, Quadratic and Real
Explore advanced Donaldson-Thomas invariants in algebraic geometry, including classical, motivic, quadratic, and real variants. Delve into virtual fundamental classes and refined invariants.
Maximal Mumford Curves and Graph Embeddings in Real Algebraic Geometry
Explore the geometric properties of MM-curves, focusing on real stable curves, hyperplane arrangements, and graph embeddings in relation to Mumford curves and their deformations.