Paola Frediani - Papers

Preprints and Publications:

39. (with Dario Faro and Antonio Lacopo); Higher Gaussian maps for special classes of curves.  arXiv:2411.12382.

38. (with Dario Faro and Antonio Lacopo); Higher Gaussian maps on the hyperelliptic locus and second fundamental form.  arXiv:2406.17408.

37. (with Elisabetta Colombo and Gian Pietro Pirola); Asymptotic directions in the moduli space of curves.  arXiv:2405.08641.

36. (with Elisabetta Colombo, Juan Carlos Naranjo and Gian Pietro Pirola); On the local geometry of the moduli space of (2,2)-threefolds in A_9.  arXiv:2310.10398.

35. Second fundamental form and higher Gaussian maps.  arXiv:2208.14794. To appear in Perspectives on four decades of Algebraic Geometry Volume 1: in Memory of Alberto Collino, Progress in Mathematics volume 351, Birkhauser.

34. (with Elisabetta Colombo, Juan Carlos Naranjo and Gian Pietro Pirola); The second fundamental form of the moduli space of cubic threefolds in A_5. arXiv:2207.13432. Épijournal Géom. Algébrique. Special volume in honour of C. Voisin, Article No. 9 (2023).

33. Abelian covers and second fundamental form.  arXiv:2105.07947. Manuscripta Math. 175, 267–291 (2024). https://doi.org/10.1007/s00229-024-01556-0.

32. (with  Gian Paolo Grosselli, Abolfazl Mohajer); Higher dimensional Shimura varieties in the Prym loci of ramified double covers.  arXiv:2101.09016. Mathematische Nachrichten, vol. 296, Issue 5, 1842-1858, 2023. DOI: 10.1002/mana.202100161.

31. (with  Elisabetta Colombo); On the dimension of totally geodesic submanifolds in the Prym loci.  arXiv:2101.05189. Boll. Unione Mat. Ital. 15 (2022), no. 1-2, 117–131. (Special issue dedicated to Fabrizio Catanese’s 70th birthday). https://doi.org/10.1007/s40574-021-00287-4.

30. (with  Gian Paolo Grosselli); Shimura curves in the Prym loci of ramified double covers.  arXiv:2007.09646. Internat. J. Math. 32 (2021), no. 14, Paper No. 2150110, 23 pp. DOI: 10.1142/S0129167X2150110X.

29. (with  Juan Carlos Naranjo, Irene Spelta); The fibers of the ramified Prym map.  arXiv:2007.02068. Communications in Contemporary Mathematics, Vol. 24, No. 5 (2022) 2150030 (30 pages). DOI: 10.1142/S0219199721500309.

28. (with  Indranil Biswas, Elisabetta Colombo and Gian Pietro Pirola); A Hodge theoretic projective structure on Riemann surfaces.  arXiv:1912.08595. J. Math. Pures. Appl. 149 (2021), 1-27.
DOI: https://doi.org/10.1016/j.matpur.2021.02.005.

27. (with  Alessandro Ghigi and Irene Spelta); Infinitely many Shimura varieties in the Jacobian locus for g \leq 4.  arXiv:1910.13245. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXII (2021), 1597-1619. DOI: 10.2422/2036-2145.201910_009.

26. (with  Gian Pietro Pirola); On the geometry of the second fundamental form of the Torelli map.  arXiv:1907.11407. Proceedings of the AMS. Vol. 149, N. 3, 2021, 1011-1024. DOI: https://doi.org/10.1090/proc/15291.

25. (with  Elisabetta Colombo); Second fundamental form of the Prym map in the ramified case.  arXiv:1812.07402.
"Galois Covers, Grothendieck-Teichmueller Theory and Dessins d'Enfants - Interactions between Geometry, Topology, Number Theory and Algebra", Springer Proceedings in Mathematics & Statistics, Vol.330, (2020).

24. (with  Paola Porru); On the bielliptic and bihyperelliptic loci.
Michigan Math. J., 69, (2020), 571-600. doi:10.1307/mmj/1580439627.  arXiv:1807.02073.

23. (with  Alessandro Ghigi and Gian Pietro Pirola); Fujita decomposition and Hodge loci.
J. Inst. Math. Jussieu (2020) 19(4), 1389-1408. doi:10.1017/S1474748018000452.  arXiv:1710.03531.

22. (with  Elisabetta Colombo); A bound on the dimension of a totally geodesic submanifold in the Prym locus.
Collectanea Mathematica, 70, n.1, (2019), 51-57. https://doi.org/10.1007/s13348-018-0215-0.  arXiv:1711.03421.

21. (with Elisabetta Colombo, Alessandro Ghigi and Matteo Penegini); Shimura curves in the Prym locus.
Communications in Contemporary Mathematics, Vol. 21, N0. 2 (2019) 1850009 (34 pages). https://doi.org/10.1142/S0219199718500098.  arXiv:1706.02364.

20. (with Frank Neumann); Etale homotopy types of moduli stacks of polarised abelian schemes,
Journal of Homotopy and Related Structures, (2016) 11 (2016), no. 4, 775-801. DOI 10.1007/s40062-016-0149-8. arXiv:1512.07544.

19. (with Matteo Penegini and Paola Porru); Shimura varieties in the Torelli locus via Galois coverings of elliptic curves.
Geometriae Dedicata 181 (2016) 177-192. DOI 10.1007/s10711-015-0118-0.  arXiv:1508.00730.

18. (with Alessandro Ghigi and Matteo Penegini); Shimura varieties in the Torelli locus via Galois coverings.
IMRN. Vol. 2015, No. 20, pp. 10595-10623.  arXiv:1402.0973,

17. (with Elisabetta Colombo and Alessandro Ghigi); On totally geodesic submanifolds in the Jacobian locus,
International Journal of Mathematics, 26 (2015), no. 1, 1550005 (21 pages). arXiv:1309.1022.

16. (with Caterina Barchielli); On the first gaussian map of Prym-canonical line bundles.  arXiv:1210.7598.
Geometriae Dedicata 170 (2014) 289-302.

15. (with Elisabetta Colombo);  On the Koszul cohomology of canonical and Prym-canonical binary curves.
Bull. London Math. Soc. 45 (2013) 1031-1040. arXiv:1207.3230

14. (with Elisabetta Colombo);  Prym map and second gaussian map for Prym-canonical line bundles. 
Advances in Mathematics, Volume 239, (2013) 47-71.  arXiv:1105.4472

13. (with Elisabetta Colombo and Giuseppe Pareschi)  Hyperplane sections of abelian surfaces.
J. Algebraic Geometry 21 (2012) 183-200. arXiv:0903.2781

12. The second Gaussian map for curves: a survey. 
Rendiconti dell'Università e del Politecnico di Torino, vol. 68, 3 (2010), 251-270.
Workshop on Hodge Theory and Algebraic Geometry.

11. (with Elisabetta Colombo); On the second Gaussian map for curves on a K3 surface.
Nagoya Math. J. Volume 199 (2010), 123-136.  arXiv:0905.2330

10. (with Elisabetta Colombo)  Siegel metric and curvature of the moduli space of curves.  
Transactions of the Amer. Math. Soc. 362 (2010), no. 3, 1231-1246.
  arXiv:0805.3425

9. (with Elisabetta Colombo) Some results on the second Gaussian map for curves.
Michigan Math. J. Vol. 58,  3 (2009), 745-758. arXiv:0805.3422

 
8. (with Fabrizio Catanese) Real structures on torus bundles and their deformations.
AMS/IP Studies in Advanced Mathematics Vol. 39, 2007. 
arXiv:0601108

7. (with Fabrizio Catanese) Deformation in the large of some complex manifolds, II. 
Recent progress on some problems in several complex variables and partial differential equations,  21-41,
Contemp. Math., 400, Amer. Math. Soc., Providence, RI, 2006. arXiv:0507508

6. Real Kodaira surfaces.  Collect. Math.  55  (2004),  no. 1, 61-96.
arXiv:0404390

 5. (with Frank Neumann) Etale homotopy types of moduli stacks of algebraic curves with symmetries.
K-Theory 30 (2003), no. 4, 315-340.arXiv:0404387

4. (with Fabrizio Catanese) Real hyperelliptic surfaces and the orbifold fundamental group.
J. Inst. Math. Jussieu 2 (2003), no. 2, 163-233.
arXiv:0012003
 
3. Real algebraic curves and real algebraic functions.
Port. Math. (N.S.) 59 (2002), no. 1, 1-35.
 
2. Monodromies of generic real algebraic functions.
Topology Appl. 99 (1999), no. 1, 67-97.
 
1. (with Fabrizio Catanese) Configurations of real and complex polynomials.
Journees de Geometrie Algebrique d'Orsay (Orsay, 1992). Asterisque No. 218 (1993), 61-93.
 
Abstract of talks:  

- Prym map and Gaussian maps,
Report No. 47/2011, Workshop: "Complex Algebraic Geometry", September 25th – October 1st, 2011, Mathematisches Forschungsinstitut Oberwolfach, 2011, 2687-2690.

- Mappa di Prym e mappe gaussiane, XIX Congresso dell'Unione Matematica Italiana, Conferenze e Comunicazioni, Zanichelli, 2011.

Theses:

Real  algebraic functions, real algebraic curves and their moduli spaces. Ph.D thesis. Dipartimento di Matematica dell'Universita' di Pisa (1998).

Sulla geometria delle applicazioni polinomiali. Tesi di laurea. Dipartimento di Matematica dell'Universita' di Pisa (1993).

Editorial Activity:  

I am a member of the Governing Board of

Annali di Matematica Pura e Applicata.

Books Edited:
E. Colombo, B. Fantechi. P. Frediani, D. Iacono, R. Pardini, Birational Geometry and Moduli Spaces, Springer INdAM Series 39, 2020.