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

Resources for graduate students

Graduate students.

Graduate student Jennifer Li studies the Kawamata--Morrison--Totaro cone conjecture.

Graduate student Angelica Simonetti studies cusp singularities.

Graduate student Feifei Xie studies cluster varieties.

Former graduate student Huy Le studied vector bundles on rational surfaces. Thesis.

Former graduate student Anna Kazanova studied degenerations of Godeaux surfaces and exceptional vector bundles. Thesis.


MATH 612: Graduate algebra II. Course website.


My research is partially supported by NSF grants DMS-1901970 and DMS-1601065.

The mirror of the cubic surface, with Mark Gross, Sean Keel, and Bernd Siebert, to appear in Proceedings of Miles Reid 70 conference, pdf.

Mirror symmetry and cluster algebras, with Sean Keel, 27pp., to appear in Proceedings of the ICM 2018, pdf.

Theta functions on varieties with effective anti-canonical class, with Mark Gross and Bernd Siebert, to appear in Mem. Amer. Math. Soc., preprint arXiv:1601.07081, 123pp., pdf.

Canonical bases for cluster algebras, with Mark Gross, Sean Keel, and Maxim Kontsevich, J. Amer. Math. Soc. 31 (2018), no. 2, 497--608, pdf.

Flipping surfaces, with Jenia Tevelev and Giancarlo Urzua, J. Algebraic Geom. 26 (2017), no. 2, 279--345, pdf.

Compact moduli spaces of surfaces and exceptional vector bundles, in Compactifying moduli spaces, Adv. Courses Math. CRM Barcelona, Birkhäuser/Springer (2016), 41--67, pdf.

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

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

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