Elena Guardo


My research is primarily in commutative algebra and algebraic geometry. It mainly focuses on the Hilbert functions, minimal graded and multigraded free resolution of schemes of distinct points and fat points whose support lies in Pn, in P1xP1 and in multiprojective spaces Pn_1x...xPn_k.

You can check out my current CV for further details about my research.


Main Papers in refereed journals

Some of these preprints are avaiblable at Mathematics ArXiv.





  1. Carlini, E., Catalisano, M.V., Favacchio, G., Guardo, E., Rational Normal Curves and Hadamard Products, Mediterranean Journal of Mathematics, 2022, 19(3), 134
  2. Ballico, E., Guardo, E., Finite 0-dimensional multiprojective schemes and their ideals, Journal of Algebra and its Applications, 2022, 2350186
  3. Favacchio G., Guardo E., Harbourne B., Migliore J., Expecting the unexpected: quantifying the persistence of unexpected Advances in Mathematics2021, 388, 107857
  4. Bujtás Cs., Gionfriddo M., Guardo E., Milazzo L., Milici S., Tuza Sz., Complex uniformly resolvable decompositions of Kv, (2021) Ars Math. Contemp. ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.) https://doi.org/10.26493/1855-3974.2288.a20 (Also available at http://amc-journal.eu)
  5. Ballico E., Favacchio G., Guardo E., Milazzo L., Thomas A.C., Steiner configurations ideals: Containment and colouring, Mathematics, Open Access Volume 9, Issue 3, Pages 1 - 15January 2021 Article number 210
  6. Ballico E., Favacchio G., Guardo E., Milazzo L. Steiner Systems and configurations of points Des. Codes Cryptogr, Open Access Volume 89, Issue 2, Pages 199 – 219 February 2021
  7. Guardo E., Kreuzer M., Tran L., Le Ngoc L. Kaehler Differentials for Fat Point Schemes $P^1 XP^1$. Journal of Commutative Algebra2021, 13(2), pp. 179–207
  8. Cooper S., Fatabbi G., Guardo E., Lorenzini A., Migliore J., Nagel U., Seceleanu A., Szpond J., Van Tuyl A. Symbolic powers of codimension two Cohen-Macaulay ideals Comm. Algebra, Vol 11(1), 1 Nov 2020, pp 4663- 4680
  9.  Catalisano M. V., Guardo E., Shin Y.S. The Waldschmidt constant of special k-configuration, J. of Pure and Applied Algebra (2020), Vol. 224(10), 106341
  10.  Carlini E., Catalisano M. V., Guardo E., Van Tuyl A., Hilbert functions of schemes of double and reduced points, J. Pure Appl. Algebra, (2020), Vol. 224(6), 106187
  11. Cooper S.M., Guardo E. Fat points, partial intersections and Hamming distance. J. Algebra Appl., (2020), 19(4), 2050071 DOI:10.1142/S0219498820500711
  12. Carlini E., Catalisano M.V., Guardo E., Van Tuyl A. Hadamard star configurations, Rocky Mountain J. Math (2019) Vol 49(2), pp 419-432
  13. Favacchio G., Guardo E., On the Betti numbers of three fat points in ℙ1 × ℙ1, J. Korean Math. Soc., 56 (2019), No. 3, pp. 751–766, doi.org/10.4134/JKMS.j180385
  14. Favacchio G., Guardo E., Picone B. Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1. J. Algebra Appl., ISSN: 0219-4988, Vol 18, Issue 4, 1 April 2019, Article number 1950073, doi: 10.1142/S0219498819500737
  15. Ballico, E, Bernardi, A, Chiantini, L, Guardo, E (2018). Bounds on tensor rank. Ann. Mat. Pura Appl., Vol 197, Issue 6, pp 1761—1785, doi: 10.1007/s10231-018-0748-6 December 2018, ISSN: 0373-3114, doi: 10.1007/s10231-018-0748-6
  16. Favacchio G., Guardo E., Migliore J. (2018), On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces. Proc. Amer. Math. Soc. (2018), vol. 146, p. 2811-2825, ISSN: 0002-9939, doi: 10.1090/proc/13981
  17. Guardo E., Tran L., Le Ngoc L. A Presentation of the Kähler Differential Module for a Fat Point Scheme in ℙn1× … × nk ITM Web Conf. Vol 20, 2018 International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics, doi.org/10.1051/itmconf/20182001007
  18. Bujtàs Cs, Gionfriddo M, Guardo E, Milazzo L, Tuza S, Voloshin V (2017). Extending bicolorings of Steiner triple system of order 2^h-1 – Taiwanese J. Math. Volume 21, Number 6 (December, 2017), 1265-1276.
  19. Favacchio G., Guardo E. (2016). Minimal free resolution of fat almost complete intersections in P1XP1. Canad. J. Math, ISSN: 0008-414X, online Nov 2, 2016 doi: http://dx.doi.org/10.4153/CJM-2016-040-4

20.   Bocci C, Cooper S, Guardo E, Harbourne B., Janssen M, Nagel U, Seceleanu A, Van Tuyl A, Vu T (2016). The Waldschmidt constant for squarefree monomial ideals. J. Algebraic Combin., vol. 44, Issue 4,  ISSN: 0925-9899, doi: 10.1007/s10801-016-0693-7

21.   Guardo E, Van Tuyl A (2015). Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1. SpringerBriefs Math., p. 1-134, MONOGRAFIA  Springer, ISBN: 978-3-319-24164-7, ISSN: 2191-8198, doi: 10.1007/978-3-319-24166-1

  1. Bocci C., Carlini E., Guardo E., Harbourne B. (2015). Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems. Oberwolfach Rep., vol. 12, p. 489-532, ISSN: 1660-8933, doi: 10.4171/OWR/2015/9

23.   Guardo E., Van Tuyl A.,On the Hilbert Function of sets of points in P1XP1XP1 Math. Proc. Cambridge Philos. Soc. Vol. 159 , Issue 1,( July 2015) pp 115-123, DOI: http://dx.doi.org/10.1017/S0305004115000249, Published online: 03 May 2015

24.   Carlini E., Guardo E., Van Tuyl A.,“Plane curves containing a star configuration” J. Pure Appl. Algebra Vol. 219, Issue 8 (August 2015) pp 3089-3700, doi:10.1016/j.jpaa.2014.12.008

25.   Carlini E., Guardo E., Van Tuyl A., “Star configurations on generic hypersurfaces.” J. Algebra 407 Pubblicato on line il 25 Marzo 2014, pp 1–20, http://dx.doi.org/10.1016/j.jalgebra.2014.02.013

26.   Gionfriddo M., Guardo E., Milazzo L., Voloshin V., “Feasible sets of small bicolorable STSs.”  Australas. J. of Combin., Volume 59 (1), Pubblicato on line nel Marzo 2014, Pages 107–119, (2014)


27.   Gionfriddo M., Guardo E., Milazzo L., – “Extending bicolorings for Steiner triple systems.” Appl. Anal. Discrete Math. 7 (2013), 225–234. doi:10.2298/AADM130827019G

28.   Guardo E., Harbourne B., Van Tuyl A., -“Asymptotic resurgences for ideals of positive dimensional subschemes of projective space”. Adv. Math., Vol 246 (2013) 114–127, http://dx.doi.org/10.1016/j.aim.2013.05.027.

29.   Guardo E., B. Harbourne, A. Van Tuyl, - “Fat lines in P3: regular versus symbolic powers” Pubblicato on line 17 Giugno 2013 , J. Algebra, Vol.390, 15 September 2013, pp 221—230, http://dx.doi.org/10.1016/j.jalgebra.2013.05.028.


30.   Guardo E., B. Harbourne, A. Van Tuyl – “Symbolic powers versus regular powers of ideals of general points in P1 x P1”,  Canad. J. Math. Vol. 65 (4), 2013 pp. 823–842 (pubblicato on line 13 Novembre 2012) http://dx.doi.org/10.4153/CJM-2012-045-3.


31.   Guardo E., A. Van Tuyl – “Classifying ACM sets of points in P1x P1 via separators”. Arch. Math., vol 99, Issue 1, pp 33—36 (2012). DOI: 10.1007/s00013-012-0404-0.


32.   Guardo E., A. Van Tuyl – “Separators of Arithmetically Cohen-Macaulay fat points in P1xP1”. J. Commut. Algebra Vol. 4, N 2, Summer 2012, pp 255-268. DOI:10.1216/JCA-2012-4-2-255

33.   Guardo E., A. Van Tuyl –“ Separators of fat points in PnxPm”.  J. Pure Appl. Algebra, 215, 1990-1998 (2011). Pubblicato on line 4 December, 2010, doi:10.1016/j.jpaa.2010.11.009


34.   Guardo E., L. Marino, A. Van Tuyl – “Separators of fat points in Pn”. – J. Algebra, Pubblicato on line 17 Luglio 2010, Volume 324, Issue 7, 1 October 2010, Pages 1492-1512 doi:10.1016/j.jalgebra.2010.07.008.

35.    Guardo E., A.Van Tuyl – “Separators of points in multiprojective space”.  Manuscripta Math. 126 (2008), no. 1.99-113 DOI: 10.1007/s00229-008-0165-z

36.   Guardo E., A. Van Tuyl: -- “ACM sets of points in Multiprojective Spaces”.  Collect. Math. 59 (2008), no. 2, 191–213. (2008) DOI: 10.1007/BF03191367


37.   Guardo E., B. Harbourne “Configuration types and cubic surfaces”.  J. Algebra 320 (2008) 3519—3533, doi: 10.1016/j.jalgebra.2008.05.032.


38.   Guardo E., Harbourne B., “Resolution of ideals of six points in P2”.  J. Algebra 318 (2007), no. 2, 619—640, doi: 10.1016/j.jalgebra.2007.09.018.


39.   Guardo E., Van Tuyl A.,“The minimal resolution of double points in P1xP1 with ACM support”.  J. Pure Appl. Algebra 211 (2007), no. 3, 784—800, doi: 10.1016/j.jpaa.2007.04.005.


40.   Guardo E., A. Van Tuyl – “Some results on fat points whose support is a complete intersection minus a point” - "Projective varieties with unexpected properties"- Siena 2004 A Volume in Memory of Giuseppe Veronese. (de Gruyter); pp 257--266 (2005), doi: 10.1515/9783110199703.


41.   Guardo E., A. Van Tuyl – “Powers of complete intersections and fat points in special position”.  Illinois J. Math. 49 (2005), no. 1, 265--279 (electronic).


42.   Guardo E. – “A Survey on Fat Points on a smooth quadric - Algebraic structures and their representations”, 61--87, Contemp. Math., 376, Amer. Math. Soc., Providence, RI, 2005, doi: http://dx.doi.org/10.1090/conm/376.


43.   Guardo E., A. Van Tuyl – “Fat points in P1xP1 and their Hilbert functions”.  Canad. J. Math. 56 (2004), no. 4, 716-741, doi: 10.4153/CJM-2004-033-0


44.   Guardo E. – “Fat Points Schemes on a smooth quadric”.  J. Pure Appl. Algebra 162 (2001), no. 2-3, 183—208, doi: 10.1016/S0022-4049(00)00123-7.


45.   M. Buckles, E. Guardo, A. Van Tuyl – “Fat Points on a generic almost complete intersection”. Le Matematiche (Catania) 55 (2000), no. 1, 191-202. Dipartimento di Matematica e Informatica dell’Università di Catania. Entrato in redazione il 1 aprile 2001


46.   M. Buckles, E. Guardo, A. Van Tuyl – “Fat Points a grid in P2”. Le Matematiche (Catania) 55 (2000), no. 1, 169-189. Dipartimento di Matematica e Informatica dell’Università di Catania. Entrato in redazione il 1 aprile 2001

47.   E. Guardo - Schemi di Fat Points - Ph.D. Thesis, Novembre 2000