Donu Arapura's Home Page
This is part of a projection of an elliptic curve to R3.
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Math 598 students click
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My preprints or postprints:
are available from the
algebraic geometry archive
or go to Google Scholar.
are online in dvi/ps/pdf format.
My (somewhat dated) survey article on fundamental groups of smooth
projective varieties is contained in the book:
Current topics in complex algebraic geometry
which is also available electronically
- Geometry of cohomology support loci for local systems I
(published in J. Alg. Geom. 1997)
- Geometry of cohomology support loci II: integrability of
Hitchin's map (1997)
- (with M. Nori)
Solvable fundamental groups of algebraic varieties
and Kaehler manifolds (published in Compositio Math. 1999)
- Building mixed Hodge structures
(in: The arithmetic and geometry of algebraic cycles,
AMS 2000 )
- (with P. Sastry) Intermediate Jacobians and Hodge Structures
of Moduli Spaces (published in Proc. Ind. Acad. Sci. 2000)
- A class of sheaves satisfying Kodaira's vanishing theorem
(published in Math. Ann. 2000)
- (with S. Archava) Kodaira dimension of symmetric powers (
published in Proc. AMS 2003)
- Hodge cycles on some moduli spaces
- (+ appendix by D. Keeler) Frobenius amplitude and strong vanishing theorems for vector
bundles (published Duke Math. J, 2004)
- The Leray spectral sequence is motivic (published in
Inventiones Math. 2005)
- Kahler Solvmanifolds (published Internat. Math. Res. Notices, 2004)
- Partial regularity and amplitude (published in
Amer. J. Math, 2006)
- (with S-J. Kang) Functoriality of the coniveau filtration
Canad. Math. Bull. (2007)
- Motivation for Hodge cycles (published in Advances in
- The Hodge conjecture for rationally connected fivefolds
- (with S-J. Kang) Coniveau and the Grothendieck group of varieties
(published in Mich. Math. J., 2006)
- (with A. Dhillon) The motive of the moduli stack of G-bundles over the
universal curve ( Proc. Ind. Acad. Sci., 2008)
- Mixed Hodge structures associated to geometric
variations (to appear in Cycles, Motives, Shimura Varieties, TIFR
- Varieties with very little transcendental cohomology
(published in Motives and Algebraic Cycles, Fields Inst. 2009)
- An abelian category of motivic sheaves (Advances in
- Frobenius Amplitude and Vanishing on Singular Spaces (to
appear, Illinois J. Math)
- (with M. Kumar) Beilinson-Hodge cycles on semiabelian
varieties (Math. Res. Let., 2009)
- The Hodge theoretic fundamental group and its cohomology
(published in Geom. of Alg. Cycles, Clay Inst. 2010)
- (with P. Baktary, J. Wlodarczyk) The combinatorial part of
the cohomology of a singular variety.
- Homomorphisms between Kaehler groups (published in
topology of algebraic varieties and singularities, AMS 2011)
- (with P. Baktary, J. Wlodarczyk)
Weights on cohomology, invariants of singularities, and dual complexes
(replaces earlier paper; published in Math. Ann.)
- Hodge theory of cyclic covers branched over a union of
hyperplanes (Can J. Math 2014)
- (with X. Chen, S-J. Kang) The smooth center of the cohomology of a singular variety (published in Hodge theory, complex geometry, and representation theory, AMS 2014)
- Decomposition of direct images of logarithmic
differentials (Internat. Math. Res. Notices 2015)
- Restrictions on the prime-to-p fundamental group of a smooth projective variety (published in Compositio 2015)
- Geometric Hodge structures with prescribed Hodge numbers
(to appear in Recent Advances in Hodge Theory, Cambridge)
- (with P. Solapurkar) A new class of surfaces with maximal Picard number.
- (with A. Dimca, R. Hain) On the fundamental groups of normal varieties (to appear in Com. Contemp Math)
- Toward the structure of fibered fundamental groups of projective varieties.
- A Lefschetz (1,1) theorem for singular varieties.
- Simpson's construction of varieties with many local systems.
- Kodaira-Saito vanishing via Higgs bundles in positive characteristic.
Arraymaker and other miscellaneous scripts and software that I've written are available
You can contact me via email at
where * should be replaced by @ , or you can
contact me by phone at (765) 494-1983, or by mail at
150 N. University Street
Dept. of Mathematics
West Lafayette, IN 47907-2067