Publications of Mark Andrea de Cataldo

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

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Preprints

• Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces
  (joint with T. Hausel and L. Migliorini) submitted.

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  Books

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

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  Journal publications

• Topology of Hitchin systems and Hodge theory of character varieties
  (joint with T. Hausel and L. Migliorini) to appear in Annals of Mathematics.
• The perverse filtration and the Lefschetz Hyperplane Theorem, II
  J. Algebraic Geometry 21 (2012) 305-345.
• What is a perverse sheaf?
  (joint with L. Migliorini) Notices of the A.M.S., Vol.57, Issue 05, 632-635. 
• The Decomposition Theorem and the topology of algebraic maps
  (joint with L. Migliorini) Bullettin of the A.M.S., Vol. 46, n.4, (2009), 535-633.
• The perverse filtration and the Lefschetz Hyperplane Theorem
  (joint with L. Migliorini) Annals of Mathematics, Vol. 171, No. 3, 2010, 2089-2113.
• 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.
• On singularities of primitive cohomology classes
  (joint with L. Migliorini) Proc. Amer.Math. Soc. 137 (2009) 3593-3600.
• Hodge-theoretic aspects of the Decomposition Theorem
  (joint with L. Migliorini) Algebraic Geometry, Seattle 2005, Proceedings of Symposia in Pure Mathematics, Vol. 80.2, 2009.
• Intersection forms, topology of algebraic maps and motivic decompositions for resolutions of threefolds
  (joint 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.
• The Hodge theory of algebraic maps
  (joint with L. Migliorini) Ann. Scient. Ec. Norm. Sup., 4e serie, t.38, 2005, p. 693-750.
• The Chow motive of semismall resolutions
  (joint with L. Migliorini) Math. Res. Letters, 11, 2004, n.2-3, 151-170.
• The Gysin map is compatible with mixed Hodge structures
  (joint with L. Migliorini) Centre des Recherches Mathematiques, CRM Proceedings and Lecture Series, vol 38, 2004.
• The Hard Lefschetz Theorem and the topology of semismall maps
  (joint with L. Migliorini) Ann.Scient.Ec.Norm.Sup., 4e serie, t.35. 2002, 759-772.
• The Chow groups and the motive of the Hilbert scheme of points on a surface
  (joint with L. Migliorini) Journal of algebra 251 (2002), 824-848.
• The Douady space of a complex surface
  (joint with L. Migliorini) Adv. in Math. 151 (2000), 283-312.
• Hilbert schemes of surfaces and Euler Characteristics
  Arch. Math 75 (2000) 59-64.
• Vanishing via lifting to second Witt vectors and a simple proof of an isotriviality result
  Journal of Algebra 219 (1999), 255-265.
• Effective non-vanishing, effective global generation
  Ann. Inst. Fourier, Grenoble 48, 5 (1998), 1359--1378.
• Singular hermitian metrics on vector bundles
  J. Reine Angew. Math. 502 (1998), 93-122.
• Codimension two nonsingular subvarieties of quadrics : scrolls and classification in degree $d\leq 10$,
  J. Math. Soc. Japan 50, no. 4 (1998), 879--902.
• Some adjunction-theoretic properties of codimension two nonsingular subvarieties of quadrics
  Can. Journ. of Math 49, 4 (1997), 675-695.
• A finiteness theorem for codimension two nonsingular subvarieties of quadrics
  Trans. Amer.Math. Soc. 349 (1997), 2359-2370.
• The genus of curves on the three dimensional quadric
  Nagoya Math. Journ., 147 (1997), 193-211.
• Projective threefolds with a hyperplane section of general type
  (joint with M. Palleschi) Geometriae Dedicata 61 (1996), 169-179.
• Polarized surfaces of positive Kodaira dimension with canonical bundle of small degree
  (joint with M. Palleschi) Forum Math. 4 (1992), 217-229
• Fibrazioni ellittiche e fibrati olomorfi
  Riv. Mat. Univ. Parma, 4, 15, (1989), 265-269.

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  Theses and dissertations

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

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Miscellanea

• 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 .
• 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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