**Personal data:**

Born in Catania (Italy) September 5, 1946

Married, with two cildren (Arianna and Elio)

**Education:**

Diploma at Scientific Liceum Catania 1964

Laurea degree University of Catania 1968

Advisor: Giovanni Dantoni

Thesis: The Arithmetic according to Peano

**Position held**:

Assistant: University of Catania October 15, 1968 – December 31, 1969

Assistant professor: University of Catania 1970 – 1978

Associated researcher: Brandeis University (Mass. USA) 1978-1980

Associated Professor: University of Catania 1980 –1982, 1983 – 1986

Visiting Professor: Northeastern University (Mass. USA) 1982

Full Professor: University of Catania 1987 – up today

**Field of general interests**:

Algebra and Geometry

**Current research interests**:

Commutative Algebra and Algebraic Geometry with special regard to Hilbert functions and graded Betti numbers for projective schemes, in particular of low dimension (zero-dimensional schemes, points on smooth quadrics, curves), or for special schemes as arithmetically Cohen Macaulay, Gorenstein or partial intersections.

**Administrative experiences**:

At the Mathematics Department of University of Catania:

President of Corso di Laurea in Mathematics: 1990 -1993

Director of the Math Library: 1994 –1996

President of the Committee for Positions at the Faculty of Sciences 1997 – 2003

Director of the PhD program of the Mathematics Department 2001 - 2003

Director of the Mathematics and Computer Science Department: November 2002-October 2005

Director of the Mathematics and Computer Science Department: November 2005-October 2008

Scientific Director of the Scuola Superiore di Catania April 2009 – up to now

**Conferences and meeting organized and co-organized**:

*- Convegno di Geometria Algebrica*, Catania May 1978

*- C.I.M.E. on Complete Intersections*, Acireale (Catania) 1983

*- General Meeting of Unione Matematici Italiani*, Catania 1991

*- Pragmatic 1997*, Catania May – June 1997

*- Syzygies Meeting*, Catania June 1997

*- Conference in honour od David Buchsbaum*, Catania-Roma-Genova April – May 1998

*- Pragmatic 1998*, Catania June 1998

*- Pragmatic 2000*, sez. I, sez.II, Catania June – July 2000

*- Conference on Commutative Algebra and Algebraic Geometry* (in honour of the 60th birthday of Silvio Greco), Catania 11-13 April 2001

*- Pragmatic 2001*, Catania 11-29 June 2001

*- Workshop on Exterior Algebra Methods and Other New Directions*, Erice 8-15 September 2001

*- Conference on zero-dimensional schemes and related topics* (in honor of Tony Geramita on the occasion of his 60th birthday) La Perla Ionica (Acireale) 6-8 Giugno 2002

*- Pragmatic 2002*, Catania 9-27 September 2002

*- Pragmatic 2003*, Catania 9-28 June 2003

*- Pragmatic 2004*, Catania 25 August-15 September 2004

*- Conference on* “Problemi e ricerche negli ultimi 50 anni in Geometria Algebrica, Algebra, Logica matematica e Didattica della matematica"(in occasione del 1° anniversario della scomparsa del Prof. Giovanni Dantoni), Catania 19-20 Gennaio 2006

*- Pragmatic 2006*, Catania 4-23 September 2006

*- Pragmatic 2007*, Catania 8-28 July 2007

- Conference on “Differential Algebra and Related Computer Algebra” in memory of prof.ssa Carrà - l 26 - 29 Marzo 2008, at Dipartimento di Matematica e Informatica, Universitò di Catania

*Pragmatic 2008*, Catania 13 July - 2 August 2008*Pragmatic 2009*, Catania 13 September - 2 October 2009

Member of the editorial board of Le Matematiche: 1996-1999

Reviewer of A.M.S.

Co-editor of special volume of Le Matematiche dedicated to Pragmatic ’97

Co-editor of Proceedings of the Meetings in honour of David Buchsbaum, special volume of JPAA (2000)

Member of G.N.S.A.G.A.: 1972 – up today

Member of Europroj: 1993 – 1998

Member of Eager: 2000 up to know

Local Director of the national Project Lauree Scientifiche (2005-2006, 2007-2009)

**Fellowships**:

“Borsa di studio per il potenziamento della Matematica”: 1965, 1966, 1967

N.A.T.O. – C. N.R. fellowship 1978/79, 1979/80

**Grants**:

M.U.R.S.T. (national project, ex 40%) 1980 – 2004

P.R.A.(local university project, ex 60%), director of the research 1989 – up today

I.N.D.A.M. (director of a joint project among the Universities of Catania, Messina and Reggio Calabria)

P.R.I.N. 2005/2007 and 2007 - 2009 (local scientific director)

**Teaching experiences:**

1) Tutoring of Geometry and Complements of Mathematics 1968-1973

2) Courses of Mathematics for Chemistry 1974-1978

3) Courses of Algebra, Superior Algebra, Algebraic Geometry, Differential Geometry

for Mathematicians 1980 up today

4) Courses of Geometry and Linear Algebra for Engineering

5) Courses of Algebra and Geometry for S.I.S.S.I.S. (school for teaching)

6) Courses of Commutative Algebra, Homological Algebra, Algebraic Geometry for

PhD Program

**Supervisor of Laurea degrees and PhD**:

1) Supervisor of more than 120 theses of Laurea Degree on various subjects in Algebra and Geometry (1975 – up today);

2) Supervisor of the PhD student Giuseppe Zappalà (1998): 0-*dimensional subschemes of irreducible curves of ***P**3;

3) Supervisor of the PhD student Elena Guardo (2000): *Fat points schemes*;

4) Supervisor of the PhD student Lucia Marino: *Separators for zero-dimensional schemes*.

- G.N.S.A.G.A. annual meeting, L’Aquila 1976

- Torino Politecnico 1977 (Hilbert algebras)

- Northeastern University (Boston Mass. USA) 1979

- Sherbrooke University (Quebec Canada) 1979

- Torino Politecnico 1980 (On the canonical element conjecture)

- Trento June1981

- Queen’s University (Kingston Ontario Canada) 1982

- Congress of U.M.I., Perugia September 1983

- University of Siena 1986

- University of Palermo 1987

- Kaiserslautern (Germany) 1988

- Nice (France) 1992

- Ravello 19992

- Ithaca (N.Y. USA) 1993

- Northeastern University, (Boston Mass. USA) October 1993

- Belaterra, Barcelona (Spagna) July 1996

- Trieste University, 1997

*- *Genova 1998* (Conference in honour od David Buchsbaum)*

- C.C.A.A.G. Messina 1999

- Workshop on Zero-dimensional schemes, Napoli 2000

- University of Messina July 2000

*- *Catania 2001 (*Conference on Commutative Algebra and Algebraic Geometry* in honour of the 60th birthday of Silvio Greco)

*- *Erice 2001 (*Workshop on Exterior Algebra Methods and Other New Directions)*

*-*Acireale 2002 (*Conference on zero-dimensional schemes and related topics* in honor of Tony Geramita on the occasion of his 60th birthday)

- Queen’s University, Kingston Ontario (Canada) July 2001

- University of Messina, December 2001

- University of Barcelona, (Spagna) March 2002

- “Current Trends in Commutative Algebra” Levico Terme (Trento, Italy) June 2002.

- Workshop on Algebraic geometry and commutative algebra (Me January 2005)

- Algebra Commutativa e Computazionale (Genova 4 e 5 Novembre 2005)

- Catania 2006 (*Conference on* “Problemi e ricerche negli ultimi 50 anni in Geometria Algebrica, Algebra, Logica matematica e Didattica della matematica" )

- University of Messina, June 2007

- Workshop on Commutative algebra , Algebraic geometry and applications to different fields - Brolo Sept 2007

- Conference on Commutative algebra, Algebraic geometry, combinatorics and applications - Capo d'Orlando (Me) Sept 2008

- Seminars on Commutative Algebra and Algebraic Geometry

at the Math Depart of University of Catania, every year since 1972 up today.

** **

**Books and Monographs**:

1) *Introduzione ai metodi omologici in Algebra Commutativa*.

Quaderni della Facoltà di Ingegneria dell’Università di Catania n. 1 (1978)

2) *Congetture omologiche in Algebra Commutativa*

Quaderni dei gruppi di ricerca del CNR (1981)

3) *Complete intersections and Golod ideals*

(by Eugene Gover with the collaboration of Alfio Ragusa)

Dipartimento di Matematica Università di Catania and Department of Mathematics of

Northeastern University (1984)

4) *Esercizi di Algebra* (Teoria degli insiemi, Teoria dei gruppi, Teoria degli anelli)

(in collaborazione con C. Sparacino)

Casa Editrice Zanichelli (1992)

5) *Corso di Algebra Lineare* (con esercizi svolti)

(in collaborazione con S. Giuffrida)

Casa Editrice Il Cigno Galileo Galilei (1998)

6) *Le classi di resto e l'aritmetica modulare. Esempi, formalizzazione, applicazioni.*

(in collaborazione con M.A. Aleo, D. Margarone, V. Panebianco, C. Zinna)

Casa Editrice La Tecnica della Scuola (2006)

**Scientific Papers**

7) *Sulla permanenza degli anelli di Krull e completamente integralmente chiusi rispetto a certi tipi*

* di omomorfismi.*

(with R. Maggioni)

Rend. Circ. Mat. Palermo (2) 24 (1975), no. 3, 255--266*.*

8) A*lgebras for which the generalized Hilbert nullstellensatz holds.*

(with R. Maggioni)

Annali dell'Università di Ferrara. Nuova Serie. Sezione VII. Scienze Matematiche, 25 (1979), 205--218.

9) *On openness of Hn-locus and semicontinuity of n-deviation.*

Proceedings of the American Mathematical Society 80 (1980), no. 2, 201--209.

10) * On some conditions of regularity, in terms of existence of a good basis of syzygies*.

(with C. Massaza)

Journal of Algebra 70 (1981), no. 2, 493--516.

11) *A homological invariant associated with the ideals of a local ring.*

Unione Matematica Italiana. Bollettino. D. Serie VI 2 (1983), no. 1, 147--166.

12)* Some conditions on the homology groups of Koszul complex.*

* * (with C. Massaza)

Pacific J. of Math. 111 (1984), no. 1, 137--161

13) *Connections between Hilbert function and geometric properties for a finite set of points in* **P**2.

(with R. Maggioni)

Le Matematiche 39 (1984), no. 1-2, 153--170 .

14) *Nonsingular curves passing through points of P2 in generic position I*

(with R. Maggioni)

Journal of Algebra 92 (1985), no. 1, 176--193, 194--207.

15) *Nonsingular curves passing through points of P2 in generic position II*

(with R. Maggioni)

Journal of Algebra 92 (1985), no. 1, 176--193, 194--207.

16) *Koszul complexes with isomorphic homology.*

* *(with E. Gover)

Math. Scand. 60 (1987), no. 1, 39--51

17) *Construction of smooth curves of ***P3 ***with assigned Hilbert function and generators’ degrees*

(with R. Maggioni)

Le Matematiche 42 (1987), no. 1-2, 195--209 (1989).

18) *On the cohomology grousp of linked schemes*

(with R. Maggioni)

Boll. Un. Mat. Ital. A. Serie VII 2 (1988), no. 2, 269--276

19) *Hilbert functions of generic plane sections of curves of ***P3**

(with R. Maggioni)

Invent. Math. 91 (1988), no. 2, 253--258.

20) *On the postulation of 0-dimensional subschemes on a smooth quadric*

(with S. Giuffrida and R. Maggioni)

Pacific J. of Math. 155 (1992), no. 2, 251--282.

21) *On the L**üroth semigroup of curves lying on a smooth quadric*

(with G. Paxia and G. Raciti)

Manuscripta Math. 75 (1992), no. 3, 225--246.

22) *Uniform position property and Hilbert function of points lying on a smooth quadric*

(with G. Paxia and G. Raciti)

Journal of Algebra 149 (1992), no. 1, 102--121.

23) *Resolutions of 0-dimensional subschemes of a smooth quadric*

* * (with S. Giuffrida and R. Maggioni)

Collection: Zero-dimensional schemes (Ravello, 1992), 191--204

Proceedings of Int. Conf. on Zero-dimensional schemes Ravello 1992 W. De Gruyter, 191-204

(1994)

24) *Generic quadric sections of irreducible curves*

(with G. Paxia)

Comm. Algebra 22 (1994), no. 5, 1843--1859.

25) *Irreducible Buchsbaum curves*

(with G. Paxia)

Comm. Algebra 23 (1995), no. 8, 3025--3031.

26) *Resolutions of generic points lying on a smooth quadric*

(with S. Giuffrida and R. Maggioni)

Manu. Math.91, 421-444 (1996)

27) *Generic quadric sections of irreducible Buchsbaum curves.*

(with G. Paxia)

Journal of Pure Appl. Algebra 119 (1997), no. 1, 97--111.

28) *Betti numbers of space curves bounded by Hilbert functions*

(with R. Maggioni)

Le Matematiche] 52 (1997), no. 1, 217--232 (1998).

29) *Postulation of subschemes of irreducible curves on a quadric surface functions*

(with G. Zappalà)

Rend.Circ.Matem. Palermo vol.48 (1999)

30) *Properties of 3-codimensional Gorenstein schemes*

(with G. Zappalà)

Comm. in Algebra, 29 (1), 303-318 (2001)

31) *Gorenstein schemes on general surfaces*

(with G. Zappalà)

Nagoya Math. J. Vol.162, 111-125 (2001)

32) *Partial intersections and graded Betti numbers*

(with G. Zappalà)

Beitrage zur Algebra und Geometrie (Contribution to Algebra and Geometry)

Vol. 44, n.1, 285-302 (2002)

33) *Partial Gorenstein in codimension 3*

(with G. Zappalà)

Proceedings of Conference on Commutative Algebra and Algebraic Geometry, Catania 11-13

April 2001, Le Matematiche 2002

34) *On some properties of partial intersection schemes*

(with G. Zappalà)

Collectanea Mathem. (Barcelona) 54, 3 (2003), 255-267

35) *Hilbert functions of saturated ideals with assigned generators' degrees*

(with G. Zappalà)

Rend. Univ. Padova vol. III (2004), 99-118

36) *On the reducibility of the postulation Hilbert scheme*

(with G. Zappalà)

Rend. Circ. Matem. di Palermo serie II, vol. LIII (2004), 401-406

37) *On subschemes of 0-dimensional schemes with given graded Betti numbers*

(with G. Zappalà)

Journal of Commutative Algebra (to appear)

*Looking for graded Betti numbers*

(with G. Zappalà)

Illinois Journal of Mathematics Vol 49 N. 2 (2005)

39) *Vanishing of Tor modules and homological dimensions of unions of aCM schemes*

* *(with G. Zappalà)

Journal of Algebra 310 (2007), 41--48.

40) *Numerical properties of fat schemes with special support*

(with G. Zappalà)

To appear on Communication in Algebra 2009

41) *Subschemes of determinantal and pfaffian projective schemes*

(with G. Zappalà)

To appear on Results in Mathematics - 2009

42) *On complete intersections contained in Cohen Macaulay and Gorenstein ideals*

(with G. Zappalà)

Accepted for publication on Algebra Colloquium

43) *A structure theorem and the graded Betti numbers for almost complete intersections*

(with G. Zappalà)

Submitted to J. Algebra

44) *A classification of arithmetically Cohen Macaulay varieties with given Hilbert function.*

(with R. Maggioni) (1985)

Dicember, 2009

Prof. Alfio Ragusa