Matteo Varbaro  


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Books
  • Joint with Winfried Bruns, Aldo Conca and Claudiu Raicu, Determinants, Groebner Bases and Cohomology, Springer Monographs in Mathematics, 2022, Springer Cham.  Artistic picture by Sergio Bianco

Articles
Preprints
  • Joint with Alessandro De Stefani and Linquan Ma, Herzog ideals and F-singularities. PDF
  • Joint with Hang Huang, Yevgeniya Tarasova and Emily Witt, Smooth Herzog projective curves. PDF
  • Joint with Vaibhav Pandey, Symbolic powers of the generic linkage of maximal minors. PDF
Published 
  • Joint with Alessandro De Stefani and Maria Evelina Rossi, From a local ring to its associated graded algebra to appear in Math. Ann.PDF
  • Joint with Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt, Lisa Seccia, Ladder determinantal varieties and their symbolic blowups, to appear in Math. Z. PDF
  • Joint with Sora Miyashita, The canonical trace of Stanley-Reisner rings that are Gorenstein on the punctured spectrum. Int. Math. Res. Not. IMRN 2025, no.12. PDF
  • Joint with Anurag Singh and Aldo Conca, Invariant rings of the special orthogonal group have nonunimodal h-vectors,  to appear in J. Alg. Appl., special issue - deticated to professor Sudhir Ghorpade on the occasion of his 60th birthday. PDF
  • Joint with Hongmiao Yu, Lefschetz duality for local cohomology, J. Algebra, Vol. 639 (2024), pp. 498-515. PDF
  • Joint with Hai Long Dao and Linquan Ma, Regularity, singularities and h-vector of graded algebras, Trans. Amer. Math. Soc., Vol. 377 (2024), pp. 2149-2167. PDF
  • Joint with Mitra Koley, Groebner deformations and F-singularities, Math. Nachr., Volume 296 (2023), pp. 2903-2917. PDF
  • Joint with Bruno Benedetti and Lisa Seccia, Hamiltonian paths, unit-interval complexes, and determinantal facet ideals, Adv. in Appl. Math., Volume 141 (2022), 55 pp. PDF 
  • Joint with Winfried Bruns and Aldo Conca, Castelnuovo-Mumford regularity and powers, Commutative Algebra, Springer, Cham, 2021, pp. 41-53. PDF
  • Gröbner deformations, Bull. Unione Mat. Ital., Volume 14, no. 1, 2021, pp.151-157. PDF
  • Joint with Claudia Polini, Claudiu Raicu and Marc Walker, Recent developements in Commutative Algebra, Lecture Notes in Mathematics 2283, 2021, Springer Cham.
  •  Joint with Parvaneh Nadi, CCM property and Lyubeznik numbers under Groebner deformations, Rendiconti dell'Istituto di Matematica dell'Università di Trieste, Volume 52, 2020, Pages 1-11. PDF
  • Joint with Alexandru Constantinescu and Emanuela De Negri, Singularities and radical initial ideals, Bull. Lond. Math. Soc. Volume 52, Issue 4, 1 August 2020, Pages 674-686. PDF
  • Joint with Aldo Conca, Square-free Groebner degenerations, Invent. Math. Volume 221, Issue 3, 1 September 2020, Pages 713-730.  PDF
  • Connectivity of hyperplane sections of domains, Comm. Algebra, Volume 47, Issue 6, 3 June 2019, Pages 2540-2547, special issue - deticated to professor Gennady Lyubeznik on the occasion of hibirthday. PDF
  • Joint with Alexandru Constantinescu and Thomas Kahle, Linear syzygies, hyperbolic Coxeter groups and regularity, Compositio Math. Vol. 155 (2019), pp. 1076-1097. PDF
  • Joint with Rahim Zaare-Nahandi, Simplicial complexes of small codimension, Proc. Amer. Math. Soc., Vol. 147 (2019), pp. 3347-3355. PDF
  • Joint with Giulio Caviglia,  Marc Chardin, Jason McCullough and Irena Peeva, Regularity of prime ideals, Math. Z., Vol. 291 (2019), pp. 421-435. PDF
  • Joint with Michela Di Marca, On the diameter of an ideal, J. Algebra, Vol. 511 (2018), pp. 471-485. PDF
  • Joint with Aldo Conca, Mostafazadehfard Maral, Anurag K. Singh, Hankel determinantal rings have rational singularities, Adv. Math., Vol. 335 (2018), pp. 111-129. PDF
  • Joint with Bruno Benedetti and Michela Di Marca, Regularity of line configurations, J. Pure Appl. Algebra, Vol. 222 (2018), pp. 2596-2608. PDF
  • Joint with Maria-Laura Torrente, Computing the Betti table of a monomial ideal: a reduction algorithm, J. Symb. Comp., Vol. 87 (2018), pp. 87-98. PDF
  • F-thresholds, integral closure and convexity, Springer INdAM Series, Vol. 20 (2017), "Homological and Computational Methods in Commutative Algebra", pp. 249-256. PDF
  •  Joint with Anurag K. Singh and Shunsuke Takagi, A Gorenstein criterion for strongly F-regular and log terminal singularities, Int. Math. Res. Not. IMRN 2017, no. 21, pp. 6484-6522. PDF
  • Joint with Bruno Benedetti and Barbara Bolognese, Regulating Hartshorne's connectedness theorem, J. Algebraic Combin., Vol. 46 (2017), pp. 33-50. PDF
  • Joint with Alexandru Constantinescu and Thomas Kahle, Linear syzygies, flag complexes, and regularity, Collect. Math., Vol. 67 (2016), pp. 357-362. PDF
  • Joint with Ines B. Henriques, Test, multiplier and invariant ideals, Adv. Math., Vol. 287 (2016), pp. 704-732. PDF
  • Joint with Le Dinh Nam, When does depth stabilize early on?, J. Algebra, Vol. 445 (2016), pp. 181-192. PDF
  • Joint with Jürgen Herzog and Leila Sharifan, An intriguing ring structure on the set of d-forms, MSRI Publication, Vol. 68 (2015), "Commutative Algebra and Noncommutative Algebraic Geometry", pp. 231-244. PDF
  • Joint with Alexandru Constantinescu, h-vectors of matroid complexes, Springer INdAM Series, Vol. 12 (2015) "Combinatorial Methods in Topology and Algebra", pp. 203-226. PDF
  • A special feature of quadratic monomial ideals. Springer INdAM Series, Vol. 12 (2015) "Combinatorial Methods in Topology and Algebra", pp. 137-142.PDF
  •  Joint with Karim Adiprasito, Afshin Goodarzi, Connectivity of pseudomanifold graphs from an algebraic point of view, C. R. Math. Acad. Sci. Paris, Vol. 353 (2015), pp. 1061-1065. PDF
  • Joint with Bruno Benedetti, On the dual graph of a Cohen-Macaulay algebra. Int. Math. Res. Not. IMRN 2015, no. 17, pp. 8085-8115. PDF
  • Joint with Winfried Bruns and Aldo Conca, Maximal minors and linear powers, J. Reine Angew. Math., Vol. 702 (2015), pp. 41-53. PDF
  • Joint with Jack Jeffries and Jonathan Montaño, Multiplicities of Classical Varieties, Proc. Lond. Math. Soc., Vol 110 (2015), pp. 1033-1055. PDF
  • Joint with Giulio Caviglia, Componentwise Regularity (I), J. Pure Appl. Algebra, Vol. 219 (2015), pp. 175-182. PDF
  • Joint with Lance E. Miller and Anurag K. Singh, The F-pure threeshold of a determinantal idal, Bull. Braz. Math. Soc., special issue - deticated to professors Steven Kleiman and Aron Simis on the occasion of their 70th birthdays, Vol. 45 (2014), pp. 767-775. PDF
  • Joint with Winfried Bruns, Partitions of single exterior type, to appear in Transform. Groups, Vol. 19 (2014), pp. 969-978. PDF
  • Joint with Giulio Caviglia and Alexandru Constantinescu, On a conjecture of Kalai, Israel J. Math., Vol. 204 (2014), pp. 469-475. PDF
  • Joint with Alexandru Constantinescu and Thomas Kahle, Generic and special constructions of pure O-sequences, Bull. Lond. Math. Soc., Vol. 46 (2014), pp. 924-942.PDF
  • Joint with Jürgen Herzog and Leila Sharifan, The possible extremal Betti numbers of a homogeneous ideal, Proc. Amer. Math. Soc. Vol. 142 (2014), pp. 1875-1891. PDF
  • Cohomological and projective dimensions, Compositio Math., Vol. 149 (2013), pp. 1203-1210. PDF
  • Joint with Winfried Bruns and Aldo Conca, Relations between the minors of a generic matrix, Adv. Math., Vol. 244 (2013), pp. 171-206. PDF
  • Joint with Alexandru Constantinescu, On the h-vectors of Cohen-Macaulay flag complexes, Math. Scand., Vol. 112 (2013), pp. 86-111. PDF
  • On the arithmetical rank of certain Segre embeddings, Trans. Amer. Math. Soc., Vol. 364 (2012), pp. 5091-5109. PDF
  • Joint with Le Dinh Nam, Cohen-Macaulayness of generically complete intersection ideals, Comm. Algebra, Vol. 40 (2012), pp. 931-945. PDF
  • Joint with Alexandru Constantinescu, Koszulness, Krull dimension and other properties of graph-related algebras, J. Algebraic Combin., Vol. 34 (2011), pp. 375-400. PDF
  • Joint with Bruno Benedetti, Unmixed graphs that are domains, Comm. Algebra, Vol. 39 (2011), pp. 2260-2267.PDF
  • Symbolic powers and matroids, Proc. Amer. Math. Soc., Vol. 139 (2011), pp. 2357-2366. PDF
  • Groebner deformations, connectedness and cohomological dimension, J. Algebra, Vol. 322 (2009), pp. 2492-2507. PDF
  • Joint with Bruno Benedetti and Alexandru Constantinescu, Dimension, depth and zero-divisors of the algebra of basic k-covers of a graph, Matematiche, Vol. LXIII (2008), pp. 117-156. PDF
  • Joint with Leila Sharifan, Graded Betti numbers and ideals with linear quotients, Matematiche, Vol. LXIII (2008), pp. 257-265. PDF
 
Other

  • Cohomological and Combinatorial Methods in the Study of Symbolic Powers and Equations defining Varieties. PhD thesis (2011). PDF
  • Joint with Winfried Bruns and Aldo Conca, Computations with Young symmetrizers, available online here (2011)