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Preprint (lavoro in andamento)


1. Schur Polynomials and Plücker degree of Schubert Varieties,  ArXiv:2107.06938, 2021



Articoli in Corso di Stampa








Invited book Review



02. "Lectures on K-theoretic computations in enumerative geometry, by A. Okounkov", invited book review, EMS Newsletter, European Math. Society, June 2019, Issue 112, p. 52--53, ISSN 1027-488X.



Articoli Pubblicati




03.  Clifford semialgebras, Rend. Circ. Mat. Palermo (2) 72 (2023), no. 2, 1197–1238 (con A. Chapman & L. Rowen)






04.  Bosonic and Fermionic Representations of Endomorphisms of Exterior Algebras, Fund. Math. 256 (2022), no. 3, 307–331 (con O. Behzad), ArXiv:2009.00479.pdf.



05. Polynomial Ring representations of endomorphisms of exterior powers, Collectanea Mathematica, Collect. Math. 73 (2022), no. 1, 107–133  (con O. Behzad, A. Contiero & R. Vidal Martins)



06. Grassmann Semialgebras and the Cayley‐Hamilton Theorem, Proc. Amer. Math. Soc. Ser. B, 7, (2020), 183-201, doi:10.1090/bproc/53,  (con L. H. Rowen);



07. Jet Bundles on Gorenstein Curves and Applications, Journal of Singularities, 21 (2020), 50-83, 2019 ArXiv:1804.04617.pdf, (con A. T. Ricolfi), 



08. Schubert Derivations on the Infinite Wedge Power, Bull Braz Math Soc, New Series, DOI:10.1007/s00574-020-00195-9 2020,  ArXiv:1901.06853.pdf, (con P. Salehyan),



09. The Cohomology of the Grassmannian is a gln-module, Communication in Algebra, 48, no. 1, 274--290  DOI: 10.1080/00927872.2019.1640240,  2020,  ArXiv:1902.03824.pdf, (con P. Salehyan),



10. Hasse-Schmidt Derivations and the Cayley‐Hamilton Theorem for Exterior Algebras, Contemporary Mathematics 733, 149--165, AMS, https://doi.org/10.1090/conm/733/14739,2019 (with I. Scherbak), ArXiv:1901.02686.pdf,



11. On Plücker Equations Characterizing Grassmann Cones,  in "Schubert Varieties, Equivariant Cohomology and Characteristic Classes", IMPANGA 15, (J. Buczyński, M. Michalek, E. Postinghel), ISBN print 978‐3‐03719‐182‐8, ISBN online 978‐3‐03719‐682‐3, DOI 10.4171/182,  102-125, 2018, ArXiv:1603.00510



12. From linear recurrence relations to linear ODEs with constant coefficients,  J. Algebra Appl. 15 (2016), no. 6, 1650109, 23 pp. (with D. Laksov), doi:/10.1142/S0219498816501097



13. The Boson-Fermion Correspondence from Linear ODEs, J. Alg. 415 (2014), 162‐183 (with P. Salehyan)




14. On generalized Wronskians, in "Contribution in Algebraic Geometry", Impanga Lecture Notes (P. Pragacz Ed.), EMS Congress Series Report, 257‐296, 2012, ISBN 978–3–03719–114–9, doi: 10.4171/114,  (with I. Scherbak), ArXiv: 1310.4683.pdf 



15. "On One property of One solution of One equations" or Linear ODE's, Wronskian and Schubert Calculus, Moscow Mat. J., 12, no. 2, Special issue in memory of V. I. Arnold, (2012) 275–291 (with I. Scherbak);                                               




16. The Wronskian and its Derivatives, Atti Acc. Peloritana dei Pericolanti, Physical,Mathematical, and Natural Sciences, 89, no. 2 (2011),14 pages,doi: 10.1478/C1C8902001;




17. Jets of Line Bundles on Curves and Wronskians, J. Pure Applied Algebra, 215 (2011),1528‐1538 doi:10.1016/j.jpaa.2010.10.006 (with C. Cumino e A. Nigro);



18. Equivariant Schubert Calculus, Ark. Mat. 48 (2010), no. 1, 41–55, doi: 10.1007/s11512–009–0093–5 (with T. Santiago);



19. Families of special Weierstrass points, C. R. Math. Acad. Sci. Paris, 347 (2009), no. 21–22, 1295–1298, doi:10.1016/j.crma.2009.09.018  (with P. Salehyan);



20. Schubert calculus on a Grassmann algebra, Canad. Math. Bull. 52 (2009), no. 2, 200–212, doi: 10.4153/CMB–2009–023–x (with T. Santiago);



21. Newton binomial formulas in Schubert calculus, Rev. Mat. Complut. 22 (2009), no. 1, 129–152 (with J. Cordovez e T. Santiago);        




22. Limits of special Weierstrass points, Int. Math. Res. Pap. IMRP 2008, no. 2, Art. ID rpn001, 65 pp., doi: 10.1093/imrp/rpn001 (with C. Cumino and E. Esteves);




23. Special ramification loci on the double product of a general curve,  Q. J. Math. 59 (2008), no. 2, 163‐187 (with C. Cumino and E. Esteves);



24. Schubert calculus via Hasse‐Schmidt derivations, Asian J. Math. 9 (2005), no. 3, 315‐321.                




25. A geometric interpretation and a new proof of a relation by Cornalba and Harris,  Special issue in honor of Steven L. Kleiman, Comm. Algebra 31 (2003), no. 8, 3753‐3770 (with E. Esteves);           




26. Families of Wronskian correspondences, Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 199‐210, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001  doi:10.1201/9780203908013.ch17



27. Limit Weierstrass schemes on stable curves with 2 irreducible components, Rend. Mat. Acc. Lincei (4) 12 (2001), 205‐228,  ISSN: 1120-6330  (with M. Coppens);




28. On the closure in Mg of smooth curves having a special Weierstrass point, Math. Scand. 88 (2001), no. 1, 41–71, doi:10.7146/math.scand.a-14313;                    



29. Derivatives of Wronskians with applications to families of special Weierstrass points, Trans. Amer. Math. Soc. 351 (1999), no. 6,  2233-2255 (with F. Ponza)



30. Weierstrass points on singular curves, Rend. Sem. Mat. Univ. Politec. Torino 55 (1997), no. 2, 145‐170 (1998) (with E. Ballico);       




31. On the monodromy of Weierstrass points on Gorenstein curves, J. Algebra 175 (1995), no. 2, 633‐643, doi:10.1006/jabr.1995.1205 (with E. Ballico);                                                         




32. On bounds for the Weierstrass weight at singular points of Gorenstein curves, Boll. Un. Mat. Ital. B (7) 9 (1995), no. 4, 901‐918 (with E. Ballico);                                                 




33. Weight sequences versus gap sequences at singular points of Gorenstein curves, Geom. Dedicata 54 (1995), no. 3, 267‐300, doi: 10.1007/BF01265343.                                          





34. Computing gaps sequences at Gorenstein singularities, Projective geometry with applications, 111‐128, Lecture Notes in Pure and Appl. Math., 166, Dekker, New York, 1994.




35. Weierstrass loci and generalizations I, Projective geometry with applications, 137‐166, Lecture Notes in Pure and Appl. Math., 166, Dekker, New York, 1994.                                           



36. Closed subschemes of Pr: remarks on the cohomology of their 1-codimensional subschemes, J. Algebra 163 (1994), no. 1, 265-280, doi:10.1006/jabr.1994.1017 (with M. Luisa Spreafico);              




37. A Remark on Griffiths' Cohomological Interpretation of Lax Equations: higher‐genus case, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 126(1992), no. 3‐4, 63‐70 (with E. Previato); 




38. Algebraic curves and differential equations: an introduction, The Curves Seminar at Queen's, Vol. VIII (Kingston, ON, 1990/1991), Exp. B, 69 pp., Queen's Papers in Pure and Appl. Math., 88, Queen's Univ., Kingston, ON, 1991 (with S. Greco);



39. An introduction to hypersymplectic vector spaces, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 124 (1990), no. 5–6, 235‐247;




40. Towards an affine approach to Kaluza‐Klein theory, Atti Sem. Mat. Fis. Univ. Modena 37 (1989), no. 1, 131‐145 (with M. Ferraris e M. Francaviglia);




41. Reducibility of G–invariant linear connections in principal G-bundles, Differential geometry and its applications (Eger, 1989), 231‐252,  Colloq. Math. Soc. János Bolyai, 56, North–Holland, Amsterdam, 1992 (with M. Ferraris e M. Francaviglia);                                




42. Principal connections from G–invariant linear connections, Boll. Un. Mat. Ital. B (7) 4  (1990), no. 4, 905‐926 (with M. Ferraris e M. Francaviglia)



43. Remarks on right‐invariant vectorfield bases in principal bundles and their applications to decomposition theorems, Rend. Sem. Mat. Univ. Politec. Torino 46 (1988), no. 3,  309‐322 (with M. Ferraris e M. Francaviglia);                                                         



44. A natural decomposition of S1‐invariant linear connections on S1‐bundles, Istit. Lombardo Accad. Sci. Lett. Rend. A 122 (1988), 65‐77 (1989) (with M. Ferraris e M. Francaviglia);



Monografie/Libri


45. From Classical to Modern Algebraic Geometry, Corrado Segre's Mastership and Legacy (edited with G. Casnati, A Conte, L. Giacardi, M. Marchisio, A. Verra), Trends in the History of Science, Birkhauser, 2016




46. Hasse‐Schmidt Derivations on Grassmann Algebras, Springer IMPA Lecture Notes n. 4, 2016, (with P. Salehyan)




47. Generic Linear Recurrent Sequences and Related Topics, 30° Colóquio Brasileiro de Matemática, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 26‐31 de Julho 2016




48. Linear ODE: an Algebraic Perspective, XXII Escola de Algebra, Salvador de Bahia, 2012, Publicações Matemáticas do IMPA, n. 40, 2012.                                                 



49. Intersection theory on moduli spaces of curves, Monografías de Matemática [Mathematical Monographs], 61, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2000; 




50. Schubert calculus: an algebraic introduction, Publicações Matemáticas do IMPA, [IMPA Mathematical Publications] 25o Colóquio Brasileiro de Matemática, [25th Brazilian Mathematics Colloquium] Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2005




51. Lezioni di Algebra Lineare e Geometria per l'Ingegneria, III Edizione, CLUT, Torino, 2012.                                                     



      



Articolo Storico




53. La Mosca di Hilbert: l'ultimo teorema di Fermat da Fermat ai nostri giorni, Associazione Subalpina Mathesis, Conferenze e Seminari  1995‐‐1996,134‐148.