Publications of Mark Andrea de Cataldo

You can view most of my papers on the AG ArXiv which is part of the Mathematics ArXiv.

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Preprints (including the ones accepted for publication)

• [P1]  The de Rham stack and the variety of very good splittings of a curve (with M. Groechenig and S. Zhang);
  to appear in Math.Res.Lett., arXiv:2211.09630.
• [P2]  Cohomology of the moduli of Higgs bundles via positive characteristic (with D. Maulik, J. Shen, S. Zhang);
  to appear in Jour.Europ.Math.Soc., arXiv:2105.03043.
• [P3]  Geometry of the logarithmic Hodge moduli space (with Andres Fernandez-Herrero) (with an Appendix joint with Andres. Fernandez-Herrero and Siqing Zhang);
  to apper in the J.London Math.Soc., arXiv:2211.06754.
• [P4]  Relative etale slices and cohomology of moduli spaces (with Andres Fernandez-Herrero, Andres Ibanez Nunez);
  to appear in Ann.Inst. Fourier, arXiv:2307.00350.
• [P5]  LOGARITHMIC NON-ABELIAN HODGE THEORY FOR CURVES IN PRIME CHARACTERISTIC (with Siqing Zhang;
  arXiv:2501.0985.
• [P5]  Hitchin fibrations are Ngo fibrations (with A. Fernandes Herrero, Mirko Mauri, Roberto Fringuelli;
  arXiv:2502.04966.

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Books

• [B1] Lectures on the Hodge theory of projective manifolds
  Imperial College Press, London, 2007.

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  Surveys and general mathematical audience

• [S4] The work of Peter Scholze.
  SCGP News, Volume XVIII, 8-11. 
• [S3] Changing Focus
  Notices of the A.M.S., May 2020, 662-663. 
• [S2] What is a perverse sheaf? (with L. Migliorini)
  Notices of the A.M.S., Vol.57 (2010), Issue 05, 632-635. 
• [S1] The Decomposition Theorem and the topology of algebraic maps (with L. Migliorini)
  Bullettin of the A.M.S., Vol. 46, n.4, (2009), 535-633.

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Research papers

• [42]  On the P=W conjecture for SLn (with D. Maulik and J. Shen);
  Selecta Math. (N.S.) 28 (2022), no. 5, Paper No. 90.
• [41]  A cohomological nonabelian Hodge theorem in positive characteristic (with S. Zhang);
  Algeb. Geom. 9 (2022), no.5, 606-632.
• [40]  Hitchin fibrations, abelian surfaces, and the P=W conjecture (with D. Maulik and J. Shen);
  J. Amer. Math. Soc. 35 (2022), no. 3, 911-953.
• [39]   Projective Completion of Moduli of t-Connections on Curves in Positive and Mixed Characteristic (with S. Zhang);
  Adv. Math. 401 (2022) Paper No. 108329, 43pp.
• [38]  Perverse Leray Filtration and Specialization with Applications to the Hitchin Morphism;
  Math.Proc. Cambridge Philos.Soc. 172 (2022), no. 2, 443-487.
• [37]  The Hodge numbers of O'Grady 10 via Ngo strings (with A. Rapagnetta and G. Sacca`)
  J. Math. Pures Appl. (9) 156 (2021), 125-178.
• [36]  A support theorem for the Hitchin fibration: the case of GLn and KC (with J. Heinloth and L. Migliorini)
  J. Reine Angew. Math. 780 (2021), 41-77.
• [35]  Compactification of Dolbeault moduli spaces
  Int. Math. Res. Not. IMRN 2021, no. 5, 3543-3570.
• [34]  The perverse filtration for the Hitchin fibration is locally constant (with D. Maulik)
  Pure Appl. Math. Q. 16 (2020), no. 5, 1441-1464.
• [33]  Frobenius semisimplicity for convolution morphims (with T. Haines and L.Li)
  Math. Z. 289 (2018), no. 1-2, 119-169.
• [32]  Decomposition theorem for semisimples
  J. Singul. 14 (2016), 194-197.
  
• [31]  A support theorem for the Hitchin fibration: the case of SL_n,
  Compos. Math. 153 (2017), no. 6, 1316-1347.
  
• [30] The combinatorics and topology of proper toric maps (with L. Migliorini and Mircea Mustata)
  J. Reine Angew. Math. 744 (2018), 133-163.
  
• [29] Proper toric maps over finite fields
  Int. Math. Res. Not. IMRN 2015, no. 24. 13106-13121
• [28] The projectors of the decomposition theorem are motivated (with L. Migliorini)
  Math. Res. Lett. Volume 22, Number 4, 1061-1088, 2015
  
• [27] Hodge-theoretic splitting mechanisms for projective maps (in appendix, a letter from P. Deligne)
  J. Singul. 7 (2013), 134-156.
• [26] Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces (with T. Hausel and L. Migliorini)
  J. Singul. 7 (2013), 23-38.
• [25] The Hodge theory of character varieties
  Current Developments in Algebraic Geometry, MSRI Publications, Volume 59, 2011.
• [24] Topology of Hitchin systems and Hodge theory of character varieties: the case A1 (with T. Hausel and L. Migliorini)
  Annals of Mathematics 175 (2012), 1329-1407.
• [23] The perverse filtration and the Lefschetz Hyperplane Theorem, II
  J. Algebraic Geometry 21 (2012) 305-345.
• [22] The perverse filtration and the Lefschetz Hyperplane Theorem (with L. Migliorini)
  Annals of Mathematics, Vol. 171, No. 3, 2010, 2089-2113.
• [21] The standard filtration on cohomology with compact supports with an appendix on the base change map and the Lefschetz hyperplane theorem
  Contemporary Mathematics, 496 (2009), Interactions of Classical and Numerical Algebraic Geometry, Bates et al. Eds., 199-220.
• [20] On singularities of primitive cohomology classes (with L. Migliorini)
  Proc. Amer.Math. Soc. 137 (2009) 3593-3600.
• [19] Hodge-theoretic aspects of the Decomposition Theorem
  (with L. Migliorini) Algebraic Geometry, Seattle 2005, Proceedings of Symposia in Pure Mathematics, Vol. 80.2, 2009.
• [18] Intersection forms, topology of algebraic maps and motivic decompositions for resolutions of threefolds (with L. Migliorini)
  in Algebraic cycles and Motives, London Mat.Soc., Lecture Notes Series, n.343, vol.1, pp.102-137, Cambridge University Press, Cambridge, UK, 2007.
• [17] The Hodge theory of algebraic maps (with L. Migliorini)
  Ann. Scient. Ec. Norm. Sup., 4e serie, t.38, 2005, p. 693-750.
• [16] The Chow motive of semismall resolutions (with L. Migliorini)
  Math. Res. Letters, 11, 2004, n.2-3, 151-170.
• [15] The Gysin map is compatible with mixed Hodge structures (with L. Migliorini)
  Centre des Recherches Mathematiques, CRM Proceedings and Lecture Series, vol 38, 2004.
• [14] The Hard Lefschetz Theorem and the topology of semismall maps (with L. Migliorini)
  Ann.Scient.Ec.Norm.Sup., 4e serie, t.35. 2002, 759-772.
• [13] The Chow groups and the motive of the Hilbert scheme of points on a surface (with L. Migliorini)
  Journal of algebra 251 (2002), 824-848.
• [12] The Douady space of a complex surface (with L. Migliorini)
  adv. in math. 151 (2000), 283-312.
• [11] Hilbert schemes of surfaces and Euler Characteristics
  Arch. Math 75 (2000) 59-64.
• [10] Vanishing via lifting to second Witt vectors and a simple proof of an isotriviality result
  Journal of Algebra 219 (1999), 255-265.
• [9] Effective non-vanishing, effective global generation
  Ann. Inst. Fourier, Grenoble 48, 5 (1998), 1359--1378.
• [8] Singular hermitian metrics on vector bundles
  J. Reine Angew. Math. 502 (1998), 93-122.
• [7] Codimension two nonsingular subvarieties of quadrics : scrolls and classification in degree $d\leq 10$,
  J. Math. Soc. Japan 50, no. 4 (1998), 879--902.
• [6] Some adjunction-theoretic properties of codimension two nonsingular subvarieties of quadrics
  Can. Journ. of Math 49, 4 (1997), 675-695.
• [5] A finiteness theorem for codimension two nonsingular subvarieties of quadrics
  Trans. Amer.Math. Soc. 349 (1997), 2359-2370.
• [4] The genus of curves on the three dimensional quadric
  Nagoya Math. Journ., 147 (1997), 193-211.
• [3] Projective threefolds with a hyperplane section of general type (with M. Palleschi)
  Geometriae Dedicata 61 (1996), 169-179.
• [2] Polarized surfaces of positive Kodaira dimension with canonical bundle of small degree (with M. Palleschi)
  Forum Math. 4 (1992), 217-229
• [1] Fibrazioni ellittiche e fibrati olomorfi
  Riv. Mat. Univ. Parma, 4, 15, (1989), 265-269.

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  Theses and dissertations

• [T2] Codimension two subvarieties of quadrics
  Ph.D. Thesis, Notre Dame 1995.
• [T1] Superficie polarizzate (S,A) con dimensione di Kodaira Postiva e A K piccolo
  Undergraduate Thesis, University of Milano, 1989.

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Miscellanea

• [M4] Lectures on perverse sheaves and the topology of algebraic varieties (2015 Park City Mathematical Institute)
• [M3] The Hodge theory of maps,
  in Hodge Theory, E. Cattani, F. El Zein, P. Griffiths and L.D. Trang Ed., Math. Notes, 49, Princeton University Press (2013), p.273-296.
  Lectures 4 and 5 of five lectures delivered by M.A. de Cataldo and L. Migliorini at the Hodge Theory summer school at ICTP, Trieste, June 2010.
• [M2] Lectures on the Hodge theory of projective manifolds
  in Hodge Theory and its applications, Proceedings of the Algebraic Geometry Summer School, ByeonSan, June 2003, Ed. J. Keum and B. Jun .
• [M1] Projective Varieties, Linear Systems and Vector Bundles
  Lecture notes of courses given by L. Ein, P. Ellia and F. Zak. Lecture 2 (with M. Bertolini) and Lecture 4. Istituto Nazionale di Alta Matematica ``F. Severi," Aracne Ed., Rome, 1994.
  

  
  

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