Omprokash Das



My research interest is in algebraic geometry. More specifically, I am interested in the birational geometry of algebraic varieties. In the recent years I have conducted research in the following topics: Singularities of the Minimal Model Program (MMP), namely, the adjunction and inversion of adjunction properties of MMP singularities, canonical bundle formula and F-singularities; the log abundance conjecture for 3-folds in positive characteristic, vanishing theorems, Fano varieties, structure of the various cones of curves on varieties and the existence of rational curves on varieties, etc.

 Currently, I am  interested in the birational geometry of surfaces and 3-folds over imperfect fields, more specifically, the minimal model program for 3-folds over imperfect fields and the ‘BAB Conjecture’ for log Fano surfaces over imperfect fields. These type of results are very useful in studying higher dimensional fibrations in positive characteristic.

My research interest also includes the following topics: The existence of flips for 3-folds in low character- istic (p ≤ 5), applications of MMP in the moduli of varieties of higher dimensions (in char 0 and p > 0), Rational Connectedness, Toric varieties, Mori-Dream spaces and GIT, etc.

 I am currently an Assistant Adjunct Professor at the Department of Mathematics, University of California, Los Angeles.

Papers and Preprints

2. On the Adjunction Formula for 3-folds in Characteristic p > 5, arXiv:1505.05903 [math.AG], 2015. Joint with Christopher Hacon. Mathematische Zeitschrift 284 (2016), no. 1-2, 255-269, MR3545494. 

3. The F -Different and a Canonical Bundle Formula, arXiv:1508.07295 [math.AG], 2015. Joint with Karl Schwede. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVII (2017), 1173-1205. 

4. On the Abundance Problem for 3-folds in Characteristic p > 5, arXiv:1610.03403 [math.AG], 2016. Joint with Joe Waldron. Submitted

5. Appendix A: Contracting the Section of a Weierstrass Threefold, an appendix to the ‘Bridgeland Stability on Blow Ups and Counterexamples’ by Cristian Martinez and Benjamin Schmidt, arXiv:1708.08567 [math.AG], 2017. Submitted

6. Kawamata-Viehweg Vanishing Theorem for del Pezzo surfaces over imperfect fields in characteristic p > 3, arXiv:1709.03237 [math.AG], 2017. Submitted

7.  Nef curves on 3-folds in characteristic p > 5. In preparation

© Omprokash Das 2016