**Math/Stat 416 students should go to
Brightspace for information about the class.**

Seminar on mixed Hodge modules

**My preprints or postprints**:

*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 Math, 2006) *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*(in Cycles, Motives, Shimura Varieties, TIFR Mumbai) *Varieties with very little transcendental cohomology*(published in Motives and Algebraic Cycles, Fields Inst. 2009)*An abelian category of motivic sheaves*(Advances in Math 2013)*Frobenius Amplitude and Vanishing on Singular Spaces*( Illinois J. Math 2011)- (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*(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*( Com. Contemp Math 2016) *Toward the structure of fibered fundamental groups of projective varieties.*(Journ. de l'Ecole Polytech. 2017)*A Lefschetz (1,1) theorem for singular varieties.**Simpson's construction of varieties with many local systems.*(Hodge theory and L^{2}analysis)*Kodaira-Saito vanishing via Higgs bundles in positive characteristic.*(Crelle's Journ. 2019)- (with J. Katz, D. B. McReynolds, P. Solapurkar)
*Integral Gassman equivalence of algebraic and hyperbolic manifolds*(Math. Zeit. 2019) *Lefschetz decompositions for eigenforms on a Kahler manifold.*(Proc. AMS 2018)- (with F. Hao, H. Li)
*Vanishing theorems for parabolic Higgs bundles*(Math. Res. Let. 2019) *Algebraic cycles on genus two modular fourfolds.*(Algebra & Numb. Theory 2019)*Motivic sheaves revisited.*-
*When are braid groups of manifolds Kahler*

*Some applications of positive characteristic techniques to vanishing theorems*(pdf file), Talk at Lipman Conf.*Higgs Bundles, Integrability, and holomorphic forms (dvi file)*(published in Motives, Polylogarithms and Hodge theory, Int'l Press 2002)*Intro to mixed Hodge modules (pdf file)*(published in Cycles, Motives and Shimura varieties, TIFR 2010)*Cohomology support loci for local systems and Higgs bundles*Talks at U. Michigan- (with S.-J. Kang)
*Kahler-de Rham cohomology and Chern classes*(Comm. Alg. 2011)

- Notes on Algebra
- Algebraic Geometry over the complex numbers (Springer)
- An introduction to differential forms (pdf file)
- Introduction to algebraic geometry (web page)
- A gallery of complex curves (web page)
- Introduction to etale cohomology
- Abelian varieties and moduli
- Homological algebra
- Purity for intersection cohomology after Deligne-Gabber

**Other links:**

- ArXiv
- The American Math Society
- Purdue math department home page
- MathSciNet
- SGA Online
- Back issues of Publ. IHES (including EGA)

Arraymaker and other miscellaneous scripts and software that I've written are available here.

You can contact me via email at
*arapura*math.purdue.edu*,
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

Purdue University

West Lafayette, IN 47907-2067

USA