Research Interests
I am a member of the algebraic geometry
group , and I study the geometry and topology of complex algebraic
varieties. My research focuses on Hodge theory, and on applications of mixed
Hodge modules in algebraic geometry.
Fall 2023 Teaching
This semester, I am teaching MAT 663 (Advanced Topics in Algebraic Geometry).
Mailing Address
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Contact Information
Office: Math Tower 4–110 (map )
Phone: (631) 632-8618
E-Mail: cschnell@math.stonybrook.edu
Bradley Dirks and I are organizing a winter school on New Applications of Mixed Hodge Modules at the Simons Center.
The deadline for applications is September 30 .
Click on the link below for details.
Upcoming Events
RTG Winter School: New Applications of Mixed Hodge Modules
Stony Brook University, January 15 to January 26, 2024
Singularities in Ann Arbor
University of Michigan, May 13 to May 17, 2024
Conference in memory of Jean-Pierre Demailly
University of Grenoble, June 3 to June 7, 2024
Conference in honor of Thomas Peternell's 70th birthday
Cetraro, Italy, June 30 to July 6, 2024
Past Events
Alpine meeting on nonpositive curvature in Kähler geometry
Centre Paul-Langevin, June 5 to June 9, 2023
International Congress of Basic Science
BIMSA, Beijing, July 16 to July 28, 2023
Noether-Lefschetz and Hodge loci
IMPA, Rio de Janeiro, August 21 to August 25, 2023
Click on the title of any paper to download a PDF file.
Preprints
A Hodge-theoretic proof of Hwang's theorem on base manifolds of Lagrangian fibrations
[with B. Bakker ]
Higher multiplier ideals
[with R. Yang ]
Hodge theory and Lagrangian fibrations on holomorphic symplectic manifolds
Degenerating complex variations of Hodge structure in dimension one
[with C. Sabbah ]
A log resolution for the theta divisor of a hyperelliptic curve
[with R. Yang ]
Published Papers
Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata
to appear in Proc. Amer. Math. Soc. [with L. Lombardi ]
On the behavior of Kodaira dimension under smooth morphisms
to appear in Algebraic Geometry [with M. Popa ]
Singular metrics and a conjecture by Campana and Peternell
to appear in Pure Appl. Math. Quart.
Finiteness for self-dual classes in integral variations of Hodge structure
Épijournal de Géométrie Algébrique, Special volume in honour of C. Voisin, Article no. 1 (2023) [with B. Bakker , Th. Grimm and J. Tsimerman ]
Correction to "Height bounds and the Siegel property"
Algebra Number Theory 17 (2023), no. 6, 1231–1237 [with M. Orr ]
Hodge modules and singular hermitian metrics
Math. Z. 303:28 (2023) [with R. Yang ]
The Fourier-Mukai transform made easy
Pure Appl. Math. Quart. 18 (2022), no. 4, 1749–1770
Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
J. Amer. Math. Soc. 34 (2021), no. 2, 315–368 [with S. Kebekus ]
Pushforwards of pluricanonical bundles under morphisms to abelian varieties
J. Eur. Math. Soc. 22 (2020), 2511–2536 [with L. Lombardi and M. Popa ]
An overview of Morihiko Saito's theory of mixed Hodge modules
In: Representation Theory, Automorphic Forms & Complex Geometry, A Tribute to Wilfried Schmid. Intl. Press, 2020, pp.27–80.
On a theorem of Campana and Păun
Épijournal de Géométrie Algébrique, Sep. 1, 2017, Vol. 1
Vanishing theorems for perverse sheaves on abelian varieties, revisited
Selecta Math. (N.S.) 24 (2018), no. 1, 63–84 [with B. Bhatt and P. Scholze ]
Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Păun
Contemp. Math. 712 (2018), 143–195 [with Ch. Hacon and M. Popa ]
Viehweg's hyperbolicity conjecture for families with maximal variation
Invent. Math. 208 (2017), no. 3, 677–713 [with M. Popa ]
Hodge modules on complex tori and generic vanishing for compact Kähler manifolds
Geometry & Topology 21 (2017), 2419–2460 [with G. Pareschi and M. Popa ]
Fields of definition of Hodge loci
London Math. Soc. Lecture Note Ser. 427 (2016), 275–291 [with M. Saito ]
On Saito's vanishing theorem
Math. Res. Lett. 23 , No. 2 (2016), pp. 499–527
On direct images of pluricanonical bundles
Algebra Number Theory 8 (2014), no. 9, 2273–2295 [with M. Popa ]
The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
J. High Energ. Phys. 1405 , 135 (2014) [with M. Douglas and D. Park ]
Holonomic D-modules on abelian varieties [Erratum ]
Inst. Hautes Études Sci. Publ. Math. 121 (2015), no. 1, 1–55
Kodaira dimension and zeros of holomorphic one-forms
Ann. of Math. 179 (2014), no. 3, 1109–1120 [with M. Popa ]
Torsion points on cohomology support loci: from D-modules to Simpson's theorem
London Math. Soc. Lecture Note Ser. 417 (2015), 405–421
Weak positivity via mixed Hodge modules
Contemp. Math. 647 (2015), 129–137
Absolute Hodge classes
In: Hodge theory. Vol. 49. Mathematical Notes. Princeton Univ. Press, 2014, pp.469–530 [with F. Charles ]
Generic vanishing theory via mixed Hodge modules
Forum Math. Sigma 1 (2013), e1, 60pp. [with M. Popa ]
Moduli of products of stable varieties
Compositio Math. 149 (2013), no. 12, 2036–2070 [with B. Bhatt , Z. Patakfalvi and W. Ho ]
The zero locus of the infinitesimal invariant
Fields Inst. Commun. 67 (2013), 589–602 [with G. Pearlstein ]
Residues and filtered D-modules
Math. Annalen 354 (2012), no. 2, 727–763
Complex-analytic Néron models for arbitrary families of intermediate Jacobians
Invent. Math. 188 (2012), no. 1, 1–81
The fundamental group is not a derived invariant
EMS Ser. Congr. Rep. 8 (2011), 279–285
Canonical cohomology as an exterior module
Pure Appl. Math. Quart. 7 (2011), no. 4, 1529–1542 [with R. Lazarsfeld and M. Popa ]
Derived invariance of the number of holomorphic 1-forms and vector fields
Ann. Sci. Éc. Norm. Supér (4) 44 (2011), no. 3, 527–536 [with M. Popa ]
A variant of Néron models over curves
Manuscripta Math. 134 (2011), no. 34, 359–375 [with M. Saito ]
Local duality and polarized Hodge modules
Publ. Math. Res. Inst. Sci. 47 (2011), no. 3, 705–725
Primitive cohomology and the tube mapping
Math. Z. 268 (2011), no. 3–4, 1069–1089
Two lectures about Mumford-Tate groups
Rend. Semin. Mat. Univ. Politec. Torino 69 (2011), no. 2, 199–216
The locus of Hodge classes in an admissible variation of mixed Hodge structure
C. R. Acad. Sci. Paris, Ser. I 348 (2010), 657–660 [with P. Brosnan and G. Pearlstein ]
Two observations about normal functions
Clay Math. Proc. 9 (2010), 75–79
Unpublished Papers
Graded duality for filtered D-modules
[with M. Saito ]
On the locus of limit Hodge classes
Surfaces with big anticanonical class
[with D. Chen ]
Canonical extensions of local systems
Idempotent ultrafilters and polynomial recurrence
Ph.D. Thesis
The boundary behavior of cohomology classes and singularities of normal functions
[Ohio State University, 2008]
Mixed Hodge modules
Claude Sabbah and I are adapting Saito's theory of mixed Hodge modules to the case of complex coefficients. A collection of notes (in progress) can be found on Claude's website .
Notes from courses and talks
Four lectures on Degenerating variations of Hodge structure in dimension one (Aussois, 2023)
A graduate course on Algebraic D-modules
(Stony Brook, 2019)
A graduate course on Basic topology (Stony Brook, 2014 and 2022)
A talk on Zeros of holomorphic one-forms (Paris, 2014)
A graduate course on the Generic vanishing theorem
(Stony Brook and Bonn, 2013)
A graduate course on Complex manifolds
(Chicago, 2010)
A seminar on Deformations of complex structure
(Columbus, 2005)
A seminar about Picard-Fuchs equations
(Columbus, 2004)
A talk on the Gauss-Bonnet theorem
(Columbus, 2004)
A lecture on the De Giorgi-Nash-Moser estimates
(Columbus, 2002)
Miscellaneous notes