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.



  1. Cooper S.M., Guardo E. Fat points, partial intersections and Hamming distance. JOURNAL OF ALGEBRA AND ITS APPLICATIONS,  (2019) In stampaDOI: 10.1142/S0219498820500711

2.      Guardo E., Kreuzer M., Tran L., Le Ngoc L. Kaehler Differentials for Fat Point Schemes $P^1 XP^1$. To appear in J. Commut. Algebra (2019) https://projecteuclid.org/euclid.jca/1545015628

3.      Carlini E., Catalisano M.V., Guardo E., Van Tuyl A. Hadamard star configurations, To appear Rocky Mount. J. Math (2019) https://projecteuclid.org/euclid.rmjm/1552186827

  1. Favacchio G., Guardo E.,On the Betti numbers of three fat points in 1 × 1 ,Journal of the Korean Mathematical Society,56 (2019), No. 3, pp. 751–766, doi.org/10.4134/JKMS.j180385

5.      Favacchio G., Guardo E., Picone B. Special arrangements of lines: Codimension 2 ACM varieties in 1 × 1 × 1. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, ISSN: 0219-4988, Vol 18, Issue 4, 1 April 2019, Article number 1950073, doi: 10.1142/S0219498819500737

  1. Ballico, E, Bernardi, A, Chiantini, L, Guardo, E (2018). Bounds on tensor rank. ANNALI DI MATEMATICA PURA ED APPLICATA, 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
  2. G. Favacchio, E. Guardo, J. Migliore (2018), On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces. Proceedings of the American Mathematical Society. (2018), vol. 146, p. 2811-2825, ISSN: 0002-9939, doi: 10.1090/proc/13981

8.      Guardo E., Tran L., Le Ngoc L. A Presentation of the Kähler Differential Module for a Fat Point Scheme in n1× … × nkITM 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

9.      Bujtàs Cs, Gionfriddo M, Guardo E, Milazzo L, Tuza S, Voloshin V (2017). Extending bicolorings of Steiner triple system of order 2^h-1 – Taiw. J. of Math. Volume 21, Number 6 (December, 2017), 1265-1276.

10.  G. Favacchio, E. Guardo (2017). Minimal free resolution of fat almost complete intersections in P1XP1. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES vol. 69(2017), no. 6, 1274-1291. http://dx.doi.org/10.4153/CJM-2016-040-4

11.  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. JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 44, Issue 4,  ISSN: 0925-9899, doi: 10.1007/s10801-016-0693-7

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

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

14.  E. Guardo, A. Van Tuyl“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

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

16.  E. Carlini, E. Guardo, A. Van Tuyl -- “Star configuration points on generic hypersurfaces”  Journal of Algebra 407 (2014) 1–20, http://dx.doi.org/10.1016/j.jalgebra.2014.02.013

17.   M. Gionfriddo, E. Guardo, L. Milazzo, V. Voloshin – Feasible sets of small bicolorable STSs  AUSTRALASIAN JOURNAL OF COMBINATORICS, Volume 59(1) (2014), Pages 107–119

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

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

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

21.  E. Guardo, 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  (published on line 13 November 2012) http://dx.doi.org/10.4153/CJM-2012-045-3

22.  E. Guardo, A. Van Tuyl - Classifying ACM sets of points in P1× P1 via separators. Archiv Der Mathematik, vol 99, Issue 1, pp 33—36 (2012), 2012. DOI: 10.1007/s00013-012-0404-0.

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

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

25.  Guardo, L. Marino, A. Van Tuyl -- Separators of fat points in PnJ. Algebra, Available online 17 July 2010, Volume 324, Issue 7, 1 October 2010, Pages 1492-1512 doi:10.1016/j.jalgebra.2010.07.008,

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

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

28.  E. Guardo, B. Harbourne -- Configuration types and cubic surfaces J. Algebra 320 (2008) 3519--3533

29.  E. Guardo, B. Harbourne -- Resolution of ideals of six points in P2 , J. Algebra 318 (2007), no. 2, 619--640.

30.  E. Guardo, A. Van Tuyl -- The minimal resolution of double points in P1xP1 with ACM support, J. Pure Appl. Algebra 211 (2007), no. 3, 784--800

31.  E. Guardo, 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)

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

33.  E. Guardo - 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.

34.  E. Guardo, A. Van Tuyl - Fat points in P1xP1 and their Hilbert functions, Canad. J. Math. 56 (2004), no. 4, 716--741.

35.  E. Guardo - Fat Points Schemes on a smooth quadric, J. Pure Appl. Algebra 162 (2001), no. 2-3, 183--208.

36.  M. Buckles, E.Guardo, A. Van Tuyl - Fat Points on a generic almost complete intersection, Matematiche (Catania) 55 (2000), no. 1, 191--202 (2001).

37.  M. Buckles, E.Guardo, A. Van Tuyl - Fat Points a grid in P2 , Matematiche (Catania) 55 (2000), no. 1, 169--189 (2001).

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

Preprints Submitted and Work in Progress

Some of these preprints are avaiblable at Mathematics ArXiv.