## 13 Citations

### Geometry of logarithmic derivations of hyperplane arrangements

- Mathematics
- 2021

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

- Mathematics
- 2011

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

- MathematicsCompositio 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

- Mathematics
- 2013

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

- Mathematics
- 2013

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

- Mathematics
- 2021

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

- Mathematics
- 2020

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…

### FREENESS OF HYPERPLANE ARRANGEMENTS AND DIVISORS

- Mathematics
- 2012

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

- Mathematics
- 2013

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…

## References

SHOWING 1-10 OF 31 REFERENCES

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

- Mathematics
- 1981

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

- Mathematics
- 2000

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

- Mathematics
- 2010

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

- Mathematics
- 1996

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

- Mathematics
- 2013

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

- MathematicsDiscret. Comput. Geom.
- 2011

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

- Mathematics
- 1996

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

- Mathematics
- 2011

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

- MathematicsNagoya Mathematical Journal
- 1995

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…