36 citations · 81 across the 17 of their papers we have counts for
23 papers
Eigenvector Varieties
Sandra Di Rocco, Bernd Sturmfels, Svala Sverrisdóttir
Any linear space of square matrices has an associated eigenvector variety. Its points are eigenvectors of matrices from that linear space. We present a systematic study of eigenvec…
Osculating Geometry and Higher-Order Distance Loci
Sandra Di Rocco, Kemal Rose, Luca Sodomaco
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Eucli…
Conditional Euclidean distance optimization via relative tangency
Sandra Di Rocco, Lukas Gustafsson, Luca Sodomaco
We introduce a theory of relative tangency for projective algebraic varieties. The dual variety of a variety relative to a subvariety is the set of hyperplanes t…
Interpolation of toric varieties
Alicia Dickenstein, Sandra Di Rocco, Ragni Piene
Let be a -dimensional variety in -dimensional projective space. Let be a positive integer such that . Consider the following in…
Computing geometric feature sizes for algebraic manifolds
Sandra Di Rocco, Parker B. Edwards, David Eklund +2
We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and the weak feature size of the real part of an equidimensional and…
Gaussian likelihood geometry of projective varieties
Sandra Di Rocco, Lukas Gustafsson, Luca Schaffler
We explore the maximum likelihood degree of a homogeneous polynomial on a projective variety , , which generalizes the concept of Gaussian maximum likelih…
Families of pointed toric varieties and degenerations
Sandra Di Rocco, Luca Schaffler
The Losev-Manin moduli space parametrizes pointed chains of projective lines. In this paper we study a possible generalization to families of pointed degenerate toric varieties. Ge…
Iterated and mixed discriminants
Alicia Dickenstein, Sandra di Rocco, Ralph Morrison
We consider systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case, the closure of the locus of coefficients giving a non-degenerate…
Discrete Mixed Volume and Hodge-Deligne Numbers
Sandra Di Rocco, Christian Haase, Benjamin Nill
Generalizing the famous Bernstein-Kushnirenko Theorem, Khovanskii proved in 1978 a combinatorial formula for the arithmetic genus of the compactification of a generic complete inte…
Negative curves on symmetric blowups of the projective plane, resurgences and Waldschmidt constants
Thomas Bauer, Sandra Di Rocco, Brian Harbourne +3
The Klein and Wiman configurations are highly symmetric configurations of lines in the projective plane arising from complex reflection groups. One noteworthy property of these con…
A note on higher order Gauss maps
Sandra Di Rocco, Kelly Jabbusch, Anders Lundman
We study Gauss maps of order , associated to a projective variety embedded in projective space via a line bundle We show that if is a smooth, complete complex varie…
Toric vector bundles and parliaments of polytopes
Sandra Di Rocco, Kelly Jabbusch, Gregory G. Smith
We introduce a collection of convex polytopes associated to a torus-equivariant vector bundle on a smooth complete toric variety. We show that the lattice points in these polytopes…
Bounded Negativity and Arrangements of Lines
Thomas Bauer, Sandra Di Rocco, Brian Harbourne +4
The Bounded Negativity Conjecture predicts that for any smooth complex surface there exists a lower bound for the selfintersection of reduced divisors on . This conjecture i…
The effect of points fattening on Hirzebruch surfaces
Sandra Di Rocco, Anders Lundman, Tomasz Szemberg
The purpose of this note is to study initial sequences of zero-dimensional subschemes of Hirzebruch surfaces and classify subschemes whose initial sequence has the minimal possible…
Linear Toric Fibrations
Sandra Di Rocco
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to giv…
Mixed Discriminants
Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein +2
The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick…
Higher order duality and toric embeddings
Alicia Dickenstein, Sandra di Rocco, Ragni Piene
The notion of higher order dual varieties of a projective variety is a natural generalization of the classical notion of projective duality, introduced by Piene in 1983. In this pa…
Polyhedral adjunction theory
Sandra Di Rocco, Christian Haase, Benjamin Nill +1
In this paper we give a combinatorial view on the adjunction theory of toric varieties. Inspired by classical adjunction theory of polarized algebraic varieties we define two conve…
Recent developments and open problems in linear series
Thomas Bauer, Cristiano Bocci, Susan Cooper +11
In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of i…
Derived category of toric fibrations
L. Costa, S. Di Rocco, R. M. Miro-Roig
The derived category of bounded complexes of coherent sheaves is one of the most important algebraic invariants of a smooth projective variety. An important approach to understand…
A primer on Seshadri constants
Thomas Bauer, Sandra Di Rocco, Brian Harbourne +4
Seshadri constants express the so called local positivity of a line bundle on a projective variety. They were introduced by Demailly. The original idea of using them towards a proo…
Cyclic coverings and higher order embeddings of algebraic varieties
Thomas Bauer, Sandra Di Rocco, Tomasz Szemberg
An algebraic variety X is embedded to the order k via a line bundle L if the global sections of L generate all (simultaneous) jets of order k on X or if they separate all zero-dime…
k-very ample line bundles on Del Pezzo Surfaces
Sandra Di Rocco
A -very ample line bundle L on a Del Pezzo Surface is numerically characterized. We find that the set of the exceptional curves and effective divisors with selfintersection zero…