19 citations · 113 across the 23 of their papers we have counts for
34 papers
Segre determinants and MHV gravity amplitudes
Joris Koefler, Emanuele Ventura, Hongmiao Yu
We describe a Segre-Veronese construction of polynomial solutions to the interpolation conditions of the numerators of tree-level MHV gravity amplitudes given by Hodges' formula. T…
A note on very ample Terracini loci
Edoardo Ballico, Emanuele Ventura
In this short note we show that, for any ample embedding of a variety of dimension at least two in a projective space, all high enough degree Veronese re-embeddings have non-empty…
On the Koiran-Skomra's question about Hessians
Edoardo Ballico, Emanuele Ventura
We give a negative answer to a question of Koiran and Skomra about Hessians, motivated by Kayal's algorithm for the equivalence problem to the Fermat polynomial. We conjecture that…
The role of Pop III stars and early black holes in the 21cm signal from Cosmic Dawn
Emanuele M. Ventura, Alessandro Trinca, Raffaella Schneider +3
Modeling the 21cm global signal from the Cosmic Dawn is challenging due to the many poorly constrained physical processes that come into play. We address this problem using the sem…
Implicitisation and Parameterisation in Polynomial Functors
Andreas Blatter, Jan Draisma, Emanuele Ventura
In earlier work, the second author showed that a closed subset of a polynomial functor can always be defined by finitely many polynomial equations. In follow-up work on $\operatorn…
Quasihomomorphisms from the integers into Hamming metrics
Jan Draisma, Rob H. Eggermont, Tim Seynnaeve +2
A function is a -quasihomomorphism if the Hamming distance between and is at most for all . We show…
Degrees of Kalman varieties of tensors
Zahra Shahidi, Luca Sodomaco, Emanuele Ventura
Kalman varieties of tensors are algebraic varieties consisting of tensors whose singular vector -tuples lay on prescribed subvarieties. They were first studied by Ottaviani and…
Strength and slice rank of forms are generically equal
Edoardo Ballico, Arthur Bik, Alessandro Oneto +1
We prove that strength and slice rank of homogeneous polynomials of degree over an algebraically closed field of characteristic zero coincide generically. To show this,…
The set of forms with bounded strength is not closed
Edoardo Ballico, Arthur Bik, Alessandro Oneto +1
The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors,…
Asymptotics of degrees and ED degrees of Segre products
Giorgio Ottaviani, Luca Sodomaco, Emuanuele Ventura
Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic…
The strength for line bundles
Edoardo Ballico, Emanuele Ventura
We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resol…
Entry loci and ranks
Edoardo Ballico, Emanuele Ventura
We study entry loci of varieties and their irreducibility from the perspective of -ranks with respect to a projective variety . These loci are the closures of the points that…
Vanishing Hessian, wild forms and their border VSP
Hang Huang, Mateusz Michałek, Emanuele Ventura
Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between…
Labels of real projective varieties
Edoardo Ballico, Emanuele Ventura
Let be a complex projective variety defined over . Recently, Bernardi and the first author introduced the notion of admissible rank with respect to . This rank ta…
Tensors with maximal symmetries
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1
We classify tensors with maximal and next to maximal dimensional symmetry groups under a natural genericity assumption (1-genericity), in dimensions greater than 7. In other words,…
Rank and border rank of Kronecker powers of tensors and Strassen's laser method
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1
We prove that the border rank of the Kronecker square of the little Coppersmith-Winograd tensor is the square of its border rank for and that the border rank of…
Geometric conditions for strict submultiplicativity of rank and border rank
Edoardo Ballico, Alessandra Bernardi, Fulvio Gesmundo +2
The -rank of a point in projective space is the minimal number of points of an algebraic variety whose linear span contains . This notion is naturally submultiplicati…
Strict inclusions of high rank loci
Edoardo Ballico, Alessandra Bernardi, Emanuele Ventura
For a given projective variety , the high rank loci are the closures of the sets of points whose -rank is higher than the generic one. We show examples of strict inclusion be…
Minimal degree equations for curves and surfaces (variations on a theme of Halphen)
Edoardo Ballico, Emanuele Ventura
Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree.…
Singular Curves of Low Degree and Multifiltrations from Osculating Spaces
Jarosław Buczyński, Nathan Ilten, Emanuele Ventura
In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occu…
The monic rank
Arthur Bik, Jan Draisma, Alessandro Oneto +1
We introduce the monic rank of a vector relative to an affine-hyperplane section of an irreducible Zariski-closed affine cone . We show that the monic rank is finite and greater…
Injective linear series of algebraic curves on quadrics
Edoardo Ballico, Emanuele Ventura
We study linear series on curves inducing injective morphisms to projective space, using zero-dimensional schemes and cohomological vanishings. Albeit projections of curves and the…
Towards a Geometric Approach to Strassen's Asymptotic Rank Conjecture
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +2
We make a first geometric study of three varieties in (for each ), including the Zariski closure of the set of tight ten…
Partially symmetric variants of Comon's problem via simultaneous rank
Fulvio Gesmundo, Alessandro Oneto, Emanuele Ventura
A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by…