Omprokash Das



My research interest is in algebraic geometry. More specifically, I am interested in the birational geometry of algebraic varieties. Currently I  am interested in the log abundance conjecture in characteristic 0 and p>0, BAB conjecture for Fano varieties in char p>0, and the existence of flips and minimal model for higher dimensional (>3) varieties in char p>0.

 

 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, DOI: 10.1007/s00209-016-1655-4.

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, MR3726839DOI: 10.2422/2036-2145.201510_012.

4. On the Abundance Problem for 3-folds in Characteristic p > 5, arXiv:1610.03403 [math.AG], 2016. Joint with Joe Waldron. Mathematische Zeitschrift, DOI: 10.1007/s00209-018-2110-5. 

5. Finiteness of Log Minimal Models and Nef curves on 3-folds in characteristic p > 5, arXiv:1711.10901 [math.AG], 2017. Nagoya Mathematical Journal, DOI: 10.1017/nmj.2018.28.

6. 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. Mathematische Zeitschrift, DOI: 10.1007/s00209-018-2149-3. 

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

8. On the Boundedness of Anti-canonical Volumes of Singular Fano

3-folds in characteristic p>5, arXiv:1808.02102 [math.AG],2018. Submitted.


Preprints in preparation

1. Log abudnace for Kahler 3-folds, joint with Wenhao Ou.

2. On 3-dimensional minimal model program for varieties over imperfect fields in char p>5, joint with Joe Waldron.



© Omprokash Das 2016