RICERCA ITALIANA     

Programmi di ricerca simili:

• 1 - Spazi di Moduli e Teoria di Lie
• 2 - VARIETA' ALGEBRICHE,TEORIA DEI MOTIVI E GEOMETRIA ARITMETICA
• 3 - Proprietà geometriche delle varietà reali e complesse
• 4 - Metriche Riemanniane e Varietà Differenziabili
• 5 - Metodi di Logica in Algebra, Analisi e Geometria
• 6 - Spazi di moduli e teorie di Lie
• 7 - Teoria dei Modelli, Teoria degli Insiemi e Applicazioni
• 8 - Strutture Geometriche, Combinatoria e loro Applicazioni
• 9 - Metodi geometrici nella teoria delle onde non lineari ed applicazioni
• 10 - Geometria noncommutativa, gruppi quantici ed applicazioni

Classificazione scientifico-disciplinare

• Area scientifico disciplinare: Scienze matematiche e informatiche
  • GEOMETRIA

Classificazione brevettuale

• FIXED CONSTRUCTIONS
  • BUILDING (layered materials, layered products in general B32B)
    • BUILDINGS OR LIKE STRUCTURES FOR PARTICULAR PURPOSES; SWIMMING OR SPLASH BATHS OR POOLS; MASTS; FENCING; TENTS OR CANOPIES, IN GENERAL (foundations E02D)
• PHYSICS
  • EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS (devices for psychotechnics or for testing reaction times A61B5/16; games, sports, amusements A63; projectors, projector screens G03B)

Classificazione geografica

• Regione: Lazio

Bibliografia

The following text is a partial bibliographical account of recent publications due to authors enrolled in the program. The quoted papers are representative of the research themes to be considered by the project as well as of the actual interest and experience in the field of the people involved. Each section of the bibliography corresponds to a research section of the project, (bearing the same letter and approximately the same title). The research sections of the project are described more in detail in 2.4.
Reading the text could be the more appropriate and helpful method for detecting the background of the project as well as its objectives and the possible evolution.
REMARKS The bibliography mainly refers to the last four years. For each section the number of references has been limited to about 10. The name of a coauthor which is not taking part to the project is followed by *.

-A- CURVES AND THEIR MODULI SPACES
[1] A.BRUNO, A.VERRA: M_15 is rationally connected, in Projective Varieties with unexpected properties 51-65, W. de Gruyter Berlin (2005)
[3] L.CAPORASO,E.SERNESI: Characterizing curves by their odd theta characteristics. J. Reine Angew. Math. 562, 101-135 (2003)
[4] L.CAPORASO, C.CASAGRANDE: Combinatorial properties of stable spin curves, Commun. Algebra 31,, 3653-3672 (2003)
[5] L.CAPORASO, C.CASAGRANDE, M.CORNALBA*: Moduli of limit roots of line bundles on a curve, to appear in Transactions of AMS (2006)
[6] L.CAPORASO: Neron models over moduli of stable curves, arXiv e-preprint AG0502171 (2005)
[7] L.CAPORASO, E.ESTEVES*: On Abel maps of stable curves, ArXiv e-preprint AG0603476 (2006)
[8] L.CAPORASO 'On certain uniformity properties of curves over function fields', Compositio Mathematica v.130 1-19 (2002)
[9] F.FLAMINI, A.KNUDSEN, G.PACIENZA*: Singular curves on a K3 surface and linear series on their normalizations", arXiv e-preprint AG/0505266, (2005),
[10] A.VERRA: The unirationality of the moduli space of curves of genus 14 and lower, Compositio Math. 141, 1425-1444 (2005)


-B- CURVES, JACOBIANS AND ABELIAN VARIETIES
[1] E. ARBARELLO*, I. KRICHEVER*, G.MARINI: Characterizing Jacobians via flexes of the Kummer variety, Mathematical Research Letters, 13 (2006), 109-123.
[2] U. BRUZZO, D. HERNANDEZ-RUIPEREZ*, Semistability vs. nefness for (Higgs) vector bundles, to appear in Diff. Geom. Appl. (2006)
[3] A. COLLINO, N. FAKHRUDDIN*, Indecomposable higher Chow cycles on Jacobians, Mathematische Zeitschrift, 240, 111-139 (2002)
[4] V. KANEV: Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)$}, Math. Nachrichten 278 154--172 (2005)
[5] G. PARESCHI, M.POPA*: Regularity on abelian varieties II: basic results on linear series and defining equations , J. Algebraic Geom. 13 (2004), 167--193.
[8] G. PARESCHI, M.POPA*: Castelnuovo theory and the geometric Schottky problem, ArXiv e-preprint AG/0407370
[9] G. PARESCHI, M.POPA*: M-regularity and the Fourier-Mukai transform, preprint math.AG/0512645
[10] R.SCHOOF Abelian varieties over Q with bad reduction in one prime only Compositio Math. vol. 141 847-868 (2005)
[11] A.VERRA, B.VAN GEEMEN*: Quaternionic Pryms and Hodge classes, Topology 42, 35-53 (2003)


-C-MODULI OF STABLE MAPS AND GROMOV-WITTEN INVARIANTS
[1] K.BEHREND*, B. FANTECHI B: The intrinsic normal cone, Inventiones Math. 128 45-88 (1997)  
[2] K BEHREND*, B. FANTECHI: Symmetric obstruction theories and Hilbert schemes of points on threefolds, preprint math.AG/0512556.
[3] V. BRAUN*, P. CANDELAS*, A. GRASSI, X. DE La OSSA*, Dualities between N=1 theories to appear in Comm. Math Physics (2006)
[4] B. FANTECHI, L GOETTSCHE: Orbifold cohomology for global quotients, Duke Math J vol 117,2003, 197-227.
[5] B. FANTECHI B., R. PANDHARIPANDE*: Stable maps and branch divisors. Compositio Math. 130 345-364 (2002)
[6] A.GRASSI, D.MORRISON*: Group representations and the Euler Characteristic of elliptically fibered Calabi-Yau threefolds, {math.AG/0005196}, Jour. of Alg. Geom., 12}, (2003) 321-356.
[7] M.GRASSI: Self-dual manifolds and mirror symmetry for the quintic threefold, Asian J. of Math. 9 (2005).
[8] T.R. RAMADAS: The Harder-Narasimhan Trace and Unitarity of the KZ/Hitchin Connection, to appear in Annals of Mathematics

-D- ALGEBRAIC SURFACES AND THEIR MODULI SPACES
[1] A. CALABRI*, C. CILIBERTO, M. MENDES LOPES*: Even sets of four nodes on rational surfaces", Mathematical Research Letters., 11 (2004), 799-808.
[2] A. CALABRI*, C. CILIBERTO, M. MENDES LOPES*: On the classification of numerically Godeaux surfaces with an involution, Transactions of the AMS.
[3] A. CALABRI*, C. CILIBERTO, F.FLAMINI, R. MIRANDA*: On the K^2 of degenerations of surfaces and the multiple point formula, to appear on Annals of Mathematics (2006), 1--43.
[4] F. GALLUZZI, G. LOMBARDO, Correspondences between K3 surfaces, with an appendix by I. Dolgachev, Michigan Math. J. (52), 267-277, 2004.
[5] C.GASBARRI, M. MCQUILLAN: Roth's theorem for ruled surfaces, Amer. J. Math. 127 (2005), no. 3, 471--492.
[6] C. HACON*, R. PARDINI: Birational characterization of products of curves of genus 2. Math. Res. Letters 12 (1) (2005). pp. 129-140 ISSN: 1073-2780
[7] M. MENDES LOPES*, R. PARDINI: The classification of surfaces with p_g=0, K^2=6 and non birational bicanonical map. Math. Annalen 329 535-552 (2004)
[8] M. MENDES LOPES*, R. PARDINI: A new family of surfaces with p_g=0 and K^2=3. Ann. Sci. Ecole Norm. Sup. 37 pp. 507-531
[9] R. PARDINI: The Severi inequality K^2>= 4chi for surfaces of maximal Albanese dimension, Inventiones Math. 153 669-672 (2005)


-E- BIRATIONAL GEOMETRY AND HIGHER DIMENSIONAL CLASSIFICATION
[1] M.BELTRAMETTI*, M.L.FANIA, A.SOMMESE* : A note on P^1-bundles as hyperplane sections, Kyushu Journal of Mathematics 59 301-306(2005)
[2] M.BERTOLINI*, M.L.FANIA: Low degree threefolds in P^6, Math. Nachrichten 278, 17-33 (2005)
[3] C.CILIBERTO, M.MELLA, F,RUSSO*: Varieties with one apparent double point, J. Alg. Geom. 13 475-512 (2004)
[4] C.CILIBERTO, F.RUSSO*: Varieties with minimal secant degree and linear systems of maximal dimension on surfaces", Advances in Math., 200 (1) 1-50 (2006)
[5] A.CORTI*, M.MELLA: On the birational geometry of quartic 3-folds I, Amer. J. Math. 126 (2004) 739-761
[6] M.MELLA On the birational geometry of quartic 3-folds II: the importance of being Q-factorial, Math. Ann. 330 (2004) 107-126
[7] P.SUPINO, G.CASNATI: Construction of threefolds with finite canonical map Glasg. Math. J. 44 65-79 (2002)



-F- PROJECTIVE GEOMETRY AND SPECIAL PROJECTIVE EMBEDDINGS
[1] E.ARRONDO*, M.L.FANIA: 'Evidence to subcanonicity of codimension two subvarieties of G(1,4)', International J. of Math., 17 157-168 (2006)
[2] V.BEORCHIA, C.CILIBERTO, V.DI GENNARO: Canonical map of low codimensional subvarieties, J. Pure and Appl. Algebra, 197, (2005) 183-212
[3] E.BALLICO, C.FONTANARI: A Terracini lemma for osculating spaces with applications to Veronese surfaces, J. Pure Appl. Algebra 195 (2005), 1-6.
[5] L.CHIANTINI, C.CILIBERTO**: The classification of defective threefolds, in Projective Varieties with unexpected properties 131-176, W. de Gruyter Berlin (2005)
[6] Ph. ELLIA, C. FOLEGATTI: On the canonical map of smooth surfaces in P4, Commun. Algebra 32, No.2, 707-713 (2004).
[7] A.F.LOPEZ, Z.RAN*, 'On the irreducibility of secant cones and an application to linear normality', Duke Math. J., 117 (2003), no. 3, 389-401.
[8] L.MANIVEL*, E.MEZZETTI: On linear spaces of skew-symmetric matrices of constant rank. Manuscripta Math. 117 (2005), no. 3, 319—331
[9] M.ROGGERO, P.VALABREGA: The speciality lemma, rank 2 bundles and Gherardelli-type theorems for surface in P^4, Comp. Math., 139, 2003, 101-111.
[10] E.SERNESI: Deformations of Algebraic Schemes, Grudlehren der Mathematischen Wissenschaft vol. 334 300 pages Springer Berlin (2006)

Parole Chiave

CURVA, SUPERFICIE ALGEBRICA, VARIETA' ABELIANA, SPAZIO DEI MODULI, MAPPE STABILI, SPAZIO DI MORI, RAZIONALMENTE CONNESSO, MAPPA BIRAZIONALE, SECANT VARIETY