A. Bernardi

发表

Decomposition of homogeneous polynomials with low rank

E. Ballico, A. Bernardi, 2010, 1003.5157.

The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition

A. Bernardi, M. V. Catalisano, A. Gimigliano, 2018, Mathematics.

Bounds on the tensor rank

L. Chiantini, E. Ballico, A. Bernardi, 2017, 1705.02299.

Real and Complex Rank for Real Symmetric Tensors with Low Ranks

E. Ballico, A. Bernardi, 2013, 1303.2457.

On the X-rank with respect to linearly normal curves

E. Ballico, A. Bernardi, 2013 .

Stratification of the fourth secant variety of Veronese varieties via the symmetric rank

E. Ballico, A. Bernardi, 2010, 1005.3465.

Tensor ranks on tangent developable of Segre varieties

E. Ballico, A. Bernardi, 2012, 1210.7976.

A comparison of different notions of ranks of symmetric tensors

B. Mourrain, A. Bernardi, Jérôme Brachat, 2012, 1210.8169.

Algebraic geometry tools for the study of entanglement: an application to spin squeezed states

I. Carusotto, A. Bernardi, 2011, 1109.0221.

On the X‐rank with respect to linear projections of projective varieties

E. Ballico, A. Bernardi, 2009, 0912.4834.

Decomposition of homogeneous polynomials over an algebraically closed field.

E. Ballico, A. Bernardi, 2010 .

On the stratification of secant varieties of Veronese varieties via symmetric rank

A. Bernardi, A. Gimigliano, M. Idà, 2009 .

Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$

E. Ballico, A. Bernardi, M. V. Catalisano, 2011, 1103.1151.

Tensor decomposition and homotopy continuation

Noah S. Daleo, B. Mourrain, J. Hauenstein, 2015, 1512.04312.

Higher secant varieties of P^n × P^m embedded in bi-degree (1,d)

A. Bernardi, M. V. Catalisano, E. Carlini, 2010, 1004.2614.

Higher secant varieties of P ^ n x P ^ m embedded in bi-degree

A. Bernardi, M. V. Catalisano, E. Carlini, 2022 .

Identi(cid:28)ability of rank-3 tensors

E. Ballico, A. Bernardi, P. Santarsiero, 2021 .

Skew-symmetric tensor decomposition

B. Mourrain, A. Bernardi, E. Arrondo, 2018, Communications in Contemporary Mathematics.

On the dimension of contact loci and the identifiability of tensors

L. Chiantini, E. Ballico, A. Bernardi, 2017, 1706.02746.

Ideals of varieties parameterized by certain symmetric tensors

Alessandra Bernardi, A. Bernardi, 2007, 0705.1942.

A note on the cactus rank for Segre–Veronese varieties

E. Ballico, A. Bernardi, Fulvio Gesmundo, 2017, Journal of Algebra.

Tensor rank on tangential variety to Segre-Veronese variety

E. Ballico, A. Bernardi, 2015 .

A uniqueness result on the decompositions of a bi-homogeneous polynomial

E. Ballico, A. Bernardi, 2015, 1507.06083.

POWER SUM DECOMPOSITION AND APOLARITY, A GEOMETRIC APPROACH. WARING PROBLEMS, SECANT VARIETIES AND SYLVESTER ALGORITHM. LECTURE NOTES

A. Bernardi, 2013 .

ON THE REGULARITY OF CACTUS SCHEMES

A. Bernardi, A. Oneto, 2021 .

Grassmann secants and linear systems of tensors

L. Chiantini, E. Ballico, A. Bernardi, 2011 .

General tensor decomposition, moment matrices and applications

P. Comon, B. Mourrain, A. Bernardi, 2011, J. Symb. Comput..

The dimension of cactus varieties of cubic forms

A. Bernardi, K. Ranestad, Joachim Jelisiejew, 2012 .

Typical and admissible ranks over fields

E. Ballico, A. Bernardi, 2016, 1604.02342.

Real and complex rank for real symmetric tensors with low complex symmetric rank

E. Ballico, A. Bernardi, 2012 .

MINIMAL DECOMPOSITION OF BINARY FORMS WITH RESPECT TO TANGENTIAL PROJECTIONS.

E. Ballico, A. Bernardi, 2010, 1007.2822.

A G ] 2 5 O ct 2 01 1 THE CACTUS RANK OF CUBIC FORMS

A. Bernardi, K. Ranestad, 2013 .

PARTIAL STRATIFICATION OF SECANT VARIETIES OF VERONESE VARIETIES VIA CURVILINEAR SUBSCHEMES

E. Ballico, A. Bernardi, 2010, 1010.3546.

A Note on plane rational curves and the associated Poncelet Surfaces

A. Bernardi, A. Gimigliano, M. Idà, 2015 .

Identifiability of Rank-3 Tensors

E. Ballico, A. Bernardi, P. Santarsiero, 2021, Mediterranean Journal of Mathematics.

Bounds on the tensor rank

L. Chiantini, E. Ballico, A. Bernardi, 2018, Annali di Matematica Pura ed Applicata (1923 -).

Dimension of Tensor Network Varieties

Claudia De Lazzari, A. Bernardi, Fulvio Gesmundo, 2021, Communications in Contemporary Mathematics.

On the partially symmetric rank of tensor products of $W$-states and other symmetric tensors

Matthias Christandl, Edoardo Ballico, Alessandra Bernardi, 2018, Rendiconti Lincei - Matematica e Applicazioni.

Geometric conditions for strict submultiplicativity of rank and border rank

E. Ballico, A. Bernardi, Fulvio Gesmundo, 2020, Annali di Matematica Pura ed Applicata (1923 -).

High order singular value decomposition for plant diversity estimation pdf

Duccio Rocchini, Martina Iannacito, Alessandra Bernardi, 2019, Bollettino dell'Unione Matematica Italiana.

Computing symmetric rank for symmetric tensors

Alessandra Bernardi, Alessandro Gimigliano, Monica Idà, 2009, J. Symb. Comput..

On real typical ranks

Grigoriy Blekherman, Giorgio Ottaviani, Alessandra Bernardi, 2015, 1512.01853.

On the variety parameterizing completely decomposable polynomials

A. Bernardi, A. Bernardi, E. Arrondo, 2009, 0903.2757.

Secant varieties to osculating varieties of Veronese embeddings of $P^n$.

A. Bernardi, M. V. Catalisano, A. Gimigliano, 2009 .

Secant varieties to osculating varieties of Veronese embeddings of $\mathbb{P}^n$

A. Bernardi, M. V. Catalisano, A. Gimigliano, 2008, 0807.2455.

On real typical ranks

G. Ottaviani, Grigoriy Blekherman, A. Bernardi, 2017, Bollettino dell'Unione Matematica Italiana.

An algorithm for the non-identifiability of rank-3 tensors

E. Ballico, A. Bernardi, P. Santarsiero, 2022, Bollettino dell'Unione Matematica Italiana.

Identifiability of Rank-3 Tensors

E. Ballico, A. Bernardi, Pierpaola Santarsiero, 2020, Mediterranean Journal of Mathematics.

GRASSMANN SECANTS, IDENTIFIABILITY, AND LINEAR SYSTEMS OF TENSORS.

L. Chiantini, E. Ballico, A. Bernardi, 2011, 1110.6367.

Multihomogeneous polynomial decomposition using moment matrices

Pierre Comon, Bernard Mourrain, Alessandra Bernardi, 2011, ISSAC '11.

rasterdiv—An Information Theory tailored R package for measuring ecosystem heterogeneity from space: To the origin and back

M. Rossini, R. Furrer, M. Schaepman, 2021, bioRxiv.

On the X-rank with respect to linearly normal curves

E. Ballico, A. Bernardi, 2011, Collectanea Mathematica.

On the X-rank with respect to linearly normal curves

E. Ballico, A. Bernardi, 2010, 1002.1578.

A note on the maximal rank

A. Bernardi, Reynaldo Staffolani, 2020, European Journal of Mathematics.

Terracini locus for three points on a Segre variety

E. Ballico, A. Bernardi, Pierpaola Santarsiero, 2020, Asian Journal of Mathematics.

A G ] 1 6 M ar 2 00 9 On the variety parametrizing completely decomposable polynomials

A. Bernardi, E. Arrondo, 2009 .

Geometric conditions for strict submultiplicativity of rank and border rank

E. Ballico, A. Bernardi, Fulvio Gesmundo, 2019, Annali di Matematica Pura ed Applicata (1923 -).

Strict inclusions of high rank loci

E. Ballico, A. Bernardi, Emanuele Ventura, 2019, J. Symb. Comput..

Typical and admissible ranks over fields

E. Ballico, A. Bernardi, 2017, Rendiconti del Circolo Matematico di Palermo Series 2.

On parameterizations of plane rational curves and their syzygies

A. Bernardi, A. Gimigliano, M. Idà, 2015, 1507.02227.

On the cactus rank of cubic forms

Kristian Ranestad, Alessandra Bernardi, A. Bernardi, 2011, J. Symb. Comput..

Higher Secant Varieties of ℙ n × ℙ1 Embedded in Bi-Degree (a, b)

E. Ballico, A. Bernardi, M. V. Catalisano, 2012 .

A new class of non-identifiable skew-symmetric tensors

A. Bernardi, D. Vanzo, Davide Vanzo, 2018, Annali di Matematica Pura ed Applicata (1923 -).

A new class of non-identifiable skew-symmetric tensors

A. Bernardi, D. Vanzo, 2016, 1606.04158.

Waring, tangential and cactus decompositions

Daniele Taufer, Alessandra Bernardi, A. Bernardi, 2018, 1812.02612.

On polynomials with given Hilbert function and applications

Kristian Ranestad, Alessandra Bernardi, Pedro Macias Marques, 2012, 1211.7306.

Unique decomposition for a polynomial of low rank

E. Ballico, A. Bernardi, 2013, 1305.1219.

On generalized Kummer of rank 3 vector bundles over a genus 2 curve

A. Bernardi, Damiano Fulghesu, 2003 .

Symmetric tensor rank with a tangent vector: a generic uniqueness theorem

E. Ballico, A. Bernardi, 2011, 1101.5090.

Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

A. Bernardi, A. Bernardi, M. V. Catalisano, 2004, Canadian Journal of Mathematics.

Some defective secant varieties to osculating varieties of Veronese surfaces

A. Bernardi, M. Catalisano, 2006 .

Tensoring by a plane maintains secant-regularity in degree at least two

E. Ballico, A. Bernardi, Tomasz Ma'ndziuk, 2023, 2312.01933.

Singularities of plane rational curves via projections

Alessandra Bernardi, Alessandro Gimigliano, Monica Idà, 2016, J. Symb. Comput..