A geometric deletion-restriction formula

  title={A geometric deletion-restriction formula},
  author={Graham C. Denham and Mehdi Garrousian and Mathias Schulze},
  journal={Advances in Mathematics},

Geometry of logarithmic derivations of hyperplane arrangements

We study the Hadamard product of the linear forms defining a hyperplane arrangement with those of its dual, which we view as generating an ideal in a certain polynomial ring. We use this ideal, which

Characteristic Polynomial of Arrangements and Multiarrangements

This thesis is on algebraic and algebraic geometry aspects of complex hyperplane arrangements and multiarrangements. We start by examining the basic properties of the logarithmic modules of all

The maximum likelihood degree of a very affine variety

  • June Huh
  • Mathematics
    Compositio Mathematica
  • 2013
Abstract We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao’s solution to Varchenko’s

The maximum likelihood degree of

We show that the maximum likelihood degree of a smooth very ane variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao’s solution to Varchenko’s conjecture

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that

Lagrangian combinatorics of matroids

The Lagrangian geometry of matroids was introduced in [ADH20] through the construction of the conormal fan of a matroid M. We used the conormal fan to give a Lagrangian-geometric interpretation of

Lagrangian geometry of matroids

We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle


This is intended to deliver as a lecture note “Arrangements in Pyrénées”. The main theme is free arrangements. We are discussing relations of freeness and splitting problems of vector bundles,

Toric and tropical compactifications of hyperplane complements

These lecture notes are based on lectures given by the author at the summer school "Arrangements in Pyr\'en\'ees" in June 2012. We survey and compare various compactifications of complex hyperplane



Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula

We define an n-arrangement as a finite family of hyperplanes through the origin in C "+1. In [11] and [12] we studied the free arrangement and defined its structure sequence (their definitions will

The module of logarithmic p-forms of a locally free arrangement

For an essential, central hyperplane arrangement A ⊆ V ≃ k n+1 we show that 1 (A) (the module of logarithmic one forms with poles along A) gives rise to a locally free sheaf on P n if and only if for

Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements

We describe dualities and complexes of logarithmic forms and differentials for central affine and corresponding projective arrangements. We generalize the Borel-Serre formula from vector bundles to

On a conjecture of V archenko

In this note we generalize and prove a recent conjecture of Varchenko concerning the number of critical points of a (multivalued) meromorphic function $\phi$ on an algebraic manifold. Under certain

Grothendieck Classes and Chern Classes of Hyperplane Arrangements

We show that the characteristic polynomial of a hyperplane arrangement can be recovered from the class in the Grothendieck group of varieties of the complement of the arrangement. This gives a quick

Projection Volumes of Hyperplane Arrangements

We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones are given by the coefficients of the characteristic polynomial of the arrangement. This

Characteristic Polynomials of Subspace Arrangements and Finite Fields

Let A be any subspace arrangement in Rndefined over the integers and let Fqdenote the finite field withqelements. Letqbe a large prime. We prove that the characteristic polynomialχ(A, q) of A counts

Quantum Integrable Model of an Arrangement of Hyperplanes

The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum

Logarithmic forms on affine arrangements

Let V be an affine of dimension l over some field K. An arrangement A is a finite collection of affine hyperplanes in V. We call A an l-arrangement when we want to emphasize the dimension of V. We