Paul Hacking

Department of Mathematics and Statistics
Lederle Graduate Research Tower, Box 34515
University of Massachusetts Amherst
Amherst, MA 01003-9305, USA

Office: LGRT 1235H
Phone: 413.545.6017

AGNES: Algebraic Geometry North Eastern Series.

Valley geometry seminar

Reading seminar in algebraic geometry

UMass Math Teaching seminar

Resources for graduate students

Graduate students.

Graduate student Huy Le studies vector bundles on rational surfaces.

Former graduate student Anna Kazanova is now a postdoc in the algebraic geometry group at U. Georgia. Her 2013 PhD thesis studies degenerations of Godeaux surfaces and exceptional vector bundles.


Math 421 Complex variables, MWF 11:15AM--12:05PM, LGRT 171. Course website.

Math 611 Graduate Algebra I, MWF 9:05AM--9:55AM, LGRT 219. Course website.

Office hours:
421: Mondays 5:00PM--6:00PM and Tuesdays 4:00PM--5:00PM
611: Mondays 3:00PM--4:00PM and Tuesdays 5:00PM--6:00PM.


My research is partially supported by NSF grant DMS-1201439.

Canonical bases for cluster algebras, with Mark Gross, Sean Keel, and Maxim Kontsevich, preprint arXiv:1411.1394, 136pp., pdf.

Flipping surfaces, with Jenia Tevelev and Giancarlo Urzua, 65 pp., to appear in J. Algebraic Geom., pdf.

Birational geometry of cluster algebras, with Mark Gross and Sean Keel, Algebr. Geom. 2 (2015), no. 2, 137--175., pdf.

Compact moduli spaces of surfaces and exceptional vector bundles, 31 pp., to appear in "Compactifying moduli spaces", Advanced Courses in Mathematics -- CRM Barcelona, Springer, pdf.

Moduli of surfaces with an anti-canonical cycle, with Mark Gross and Sean Keel, Compos. Math. 151 (2015), no. 2, 265--291, pdf.

Exceptional bundles associated to degenerations of surfaces, Duke Math. J. 162 (2013), no. 6, 1171--1202, pdf.

Mirror symmetry for log Calabi-Yau surfaces I, with Mark Gross and Sean Keel, Publ. Math. Inst. Hautes Études Sci. 122 (2015), 65--168, pdf.

Compact moduli of surfaces of general type, Contemp. Math. 564 (2012), 1--18, pdf.

Smoothable del Pezzo surfaces with quotient singularities, with Yuri Prokhorov, Compositio Math. 146 (2010), no. 1, 169--192, pdf.

Lectures on flips and minimal models, with Alessio Corti, János Kollár, Robert Lazarsfeld, and Mircea Mustaţă, in Analytic and Algebraic Geometry: Common Problems, Different Methods, IAS/Park City Math. Ser. 17 (2010), p.557--582, pdf.

Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces, with Sean Keel and Jenia Tevelev, Invent. Math. 178 (2009), no. 1, 173--227, pdf.

Canonical singularities of orders over surfaces, with Daniel Chan and Colin Ingalls, Proc. Lond. Math. Soc. (3) 98 (2009), no. 1, 83--115, pdf.

The moduli space of curves is rigid, Algebra and Number Theory 2 (2008), no. 7, 809--818, pdf.

Homology of tropical varieties, Collect. Math. 59 (2008), no. 3, 263--273, pdf.

Compactification of the moduli space of hyperplane arrangements, with Sean Keel and Jenia Tevelev, J. Algebraic Geom. 15 (2006), 657--680, pdf.

Compact moduli of plane curves, Duke Math. J. 124 (2004), no. 2, 213--257, pdf.

Semistable divisorial contractions, J. Algebra 278 (2004), no. 1, 173--186, pdf.

Lecture Notes.

Algebraic curves and Riemann surfaces (2008), 59pp., pdf.

Compact complex surfaces (2009), 84pp., pdf.

Other resources.

Past course webpages.

Return to UMass Mathematics Department.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).