Algebraic Geometry, Complex Analysis and Geometry, Differential Geometry

The researches carried out by this group cover problems of great interest in contemporary Geometry, Analysis and Topology of Real and Complex Manifolds. The specific issues that are object of the researches belong to several fields such as Complex Analysis, Function Theory, Complex Differential Geometry, Algebraic Geometry, and their applications.

Part of the research program aims at studying methods of symbolic computation, in order to identify and verify significant results in some of the subjects and, at the same time, in order to draw the attention to the computational tools used.

Training through research is a fundamental part of the activity.


Fiammetta Battaglia (Info and publications)
Paolo de Bartolomeis (Info and publications)
Alberto Dolcetti (Info and publications)
Graziano Gentili (Info and publications)
Marco Maggesi (Info and publications)
Antonella Nannicini (Info and publications)
Giorgio Ottaviani (Info and publications)
Giorgio Patrizio (Info and publications)
Fabio Podestà (Info and publications)
Elisa Prato (Info and publications)
Elena Rubei (Info and publications)
Luisella Verdi (Info and publications)
Luigi Verdiani (Info and publications)
Gabriele Vezzosi (Info and publications)
Fabio Vlacci (Info and publications)

Ph.D. and Post-Doctoral Students
Paolo Aceto
Elena Angelini
Agnese Baldisserri
Maurizio Banchi
Giulia Sarfatti
Leone Slavich
Herman Stel
Irene Vignozzi


The list of our past and forthcoming seminars.

(last update March 2012)

F. Podestà, L. Bedulli, A. Gori, Homogeneous Hypercomplex manifolds and the Joyce examples, Differential Geom. And its Appl. , 29 (2011), 547-554

F. Podestà, A. Spiro, Six-dimensional nearly Kaehler manifolds of cohomogeneity one, J. Geom. Phys. 60 (2010), 156-164

F. Podestà, L. Bedulli, A. Gori, Maximal totally complex submanifolds of HPn: homogeneity and normal holonomy , Bull London Math. Soc. 41 (2009), 1029-1040

F. Podestà, A. Spiro, Kähler-Ricci solitons on homogeneous toric bundles, J. Reine Angew. Math. 642 (2010) 109-127

F. Podestà, Homogeneous Lagrangian submanifolds of positive Euler characteristic Forum Math. 22 (2010) 949–957

L. Verdiani, W. Ziller, Positively curved homogeneous metrics on spheres, Math. Zeit. 261 (2009), 473-488

K. Grove, L. Verdiani, W. Ziller: An exotic $T^1S^4$ with positive curvature, Geom. Funct. Anal. 21 (2011), 499-524

E. Prato, The Pentagram: from the Goddess to Symplectic Geometry, Proc. Bridges (2007), 123-126

F. Battaglia, Convex Polytopes and Quasilattices from the Symplectic Viewpoint, Commun. Math. Phys, 269, (2007), 283-310

F. Battaglia, Complex quotients by nonclosed groups and their stratifications. C. R. Math. Rep. Acad. Sci. Canada Vol. 29 (2007), 33-40

F. Battaglia, E. Prato, The Symplectic Geometry of Penrose Rhombus Tilings, J. Symplectic Geom. 6 (2008), 139-158.

F. Battaglia, E. Prato, The Symplectic Penrose Kite, Comm. Math. Phys. 299 (2010), 577-601

F. Battaglia, Betti numbers of the geometric spaces associated to nonrational simple convex polytopes, Proc. Amer. Math. Soc. 139 (2011), 2309-2315.

F. Battaglia, Geometric spaces from arbitrary convex polytopes, International Journal of Mathematics, Vol. 23, No. 1 (2012), article ID: 1250013, 39 pages

P. de Bartolomeis, F. Meylan, An Intrisic Deformation Theory of CR Structures, Annali Scuola Normale Superiore, Pisa, Cl. Sci(5), Vol IX (2010), 459-494

A. Nannicini, Almost complex structures on cotangent bundles and generalized geometry, Journal of Geometry and Physics, 60 (2010), 1781-1791

R. Stangarone, L. Verdi. Cryptosystems involving one-factorizations of graphs. JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, vol. 12 (2009), 737-743,

A. Nannicini, L. Verdi, S. Vessella. note ed esercizi svolti di Calcolo 1. BOLOGNA:PITAGORA EDITRICE (2008)

G. Ciolli; A. Dolcetti. Classification of arithmetically Gorenstein divisors on some Fano varieties. ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 188 (2009), 611-617

H. Abo, G. Ottaviani, C. Peterson, Non-Defectivity of Grassmannians of planes, J. of Alg. Geom., 21, (2012) , 1-20

G. Ottaviani, E. Sernesi, On the hypersurface of Lueroth quartics, Michigan Math. J. 59 (2010), 365–394

H. Abo, G. Ottaviani, C. Peterson, Induction for secant varieties of Segre varieties, Trans. Amer. Math. Soc. 361 (2009) 767-792

C. Brambilla, G. Ottaviani, On the Alexander-Hirschowitz Theorem, J. Pure Appl. Algebra, 212 (2008), 1229-1251

E. Rubei, Resolutions of Segre emebeddings of projective spaces of any dimension, Journal of Pure and Applied Algebra 208 (2007) , 29-37

E. Rubei, A note on trees and codes, International Journal of Pure and Applied Mathematics 71 no.1, (2011), 49-56

E. Rubei, Sets of double and triple weights of trees, Annals of Combinatorics 15 no.4 (2011), 723-734

M. Chan, A.N. Jensen, E. Rubei, The 4x4 minors of a 5xn matrix are a tropical basis, Linear Algebra and its Applications 435 (7)(2011), 1598-1611

C. Bisi, G. Gentili, Boundary construction of petals at the Wolff point in the parabolic case, J. Anal. Math., 104 (2008), 1-11.

G. Gentili, F. Vlacci, Rigidity for regular functions over Hamilton and Cayley numbers and a boundary Schwarz' Lemma, Indag. Math. (N.S.), 19(4) (2008), 535-545

G. Gentili, C. Stoppato. Power series and analyticity over the quaternions. MATHEMATISCHE ANNALEN, vol. 352(1) (2012), 113-131

G. Gentili, D. Struppa. Lower bounds for polynomials of a quaternionic variable. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 140 (2012), 1659-1668

G. Gentili, I. Vignozzi. The Weierstrass Factorization Theorem for slice regular functions over the quaternions. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, vol. 40(4) (2011), 435-466

F. Colombo, G. Gentili, I. Sabadini, D. Struppa. Non commutative functional calculus: unbounded operators. JOURNAL OF GEOMETRY AND PHYSICS, vol. 60 (2010, 251-259

F.Colombo, G. Gentili, I.Sabadini, D.Struppa. Extension results for slice regular functions of a quaternionic variable. ADVANCES IN MATHEMATICS, vol. 222; (2009), 1793-1808

F. Vlacci, The Argument Principle for Slice-Regular Functions, Mich. Math. J. 60, (2011), 67-77

G. Gentili, F. Vlacci, On fixed points of slice regular quaternionic Moebius transformations, Contemporary Mathematics, 553 (2011), 75-82

F. Vlacci, The Gauss Lucas Theorem for Quaternionic Regular Polynomials, in: Hypercomplex Analysis and its Applications, Trends in Mathematics, 275-282, Birkhauser, Basel (2011)

M. Kalka, G. Patrizio, Finite type Monge-Ampère foliations, Advances in Geometry 8 (2008), 491-502

F. Bracci, G. Patrizio, S. Trapani, The pluricomplex Poisson Kernel for strongly convex domains, Transaction AMS 361 (2009), 979-1005

G. Patrizio, A. Spiro, Monge-Ampère Equations and Moduli Space for Manifolds of Circular Type, Advances in Mathematics 223 (2010), 174-197

M. Kalka, G. Patrizio, Monge-Ampère Foliations for degenerate solutions, Annali di Matematica Pura e Appl. 189 (2010), 381-393

G. Patrizio, A. Spiro, Foliations by stationary discs of almost complex domains, Bulletin des Sciences Mathématiques 134 (2010), 215-234

M. Landucci, A. Spiro, On the localization principle for the automorphisms of pseudoellipsoids, Proc. Am. Math. Soc. vol.137(4)(2009), 1339-1345

G. Ciolli, G. Gentili, M. Maggesi, A certified proof of the Cartan Fixed Point Theorems, Journal of Automated Reasoning, vol. 47(3)(2011), pp. 319-336

A. Hirschowitz, M. Maggesi, Nested Abstract Syntax in Coq, Journal of Automated Reasoning (2010), pp. 1-18

A. Hirschowitz, M. Maggesi, Modules over Monads and Initial Semantics, Information and Computation, Vol. 208, Issue 5(2010) 395-604.